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[[640,20,32]] d ≤
n
640
k
20
d
32
kd²/n
32.0
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 32, d_Z ≤ 32 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 32 · witness weight 32 (claimed upper_bound)
witness found by @vprusso · verify/gf2_fast distance_rand_witness (laptop, 3 x 400,000 trials) · found at 1.2×106 trials · survived 5×107 trials · 2026-09-26
witness operator (support, 32 qubits)
[2, 12, 22, 32, 44, 54, 64, 74, 82, 92, 102, 112, 169, 179, 189, 199, 360, 368, 370, 378, 380, 388, 390, 398, 523, 533, 543, 553, 605, 615, 625, 635]
d_Z 32 · witness weight 32 (claimed upper_bound)
witness found by @vprusso · verify/gf2_fast distance_rand_witness (laptop, 3 x 400,000 trials) · found at 1.2×106 trials · survived 5×107 trials · 2026-09-26
witness operator (support, 32 qubits)
[51, 71, 123, 126, 138, 143, 146, 158, 211, 231, 283, 286, 298, 303, 306, 318, 331, 351, 379, 399, 401, 414, 421, 434, 481, 501, 529, 549, 564, 571, 584, 591]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 8 · H_Z 8
qubit degrees H_X 4 · H_Z 4
trapping sets H_X (1,4)×640 (2,4)×80 (3,6)×5280 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 640 (2,4): 80 (2,6): 8800 (3,6): 5280 (3,8): 173440 (3,10): 16960
trapping sets H_Z (1,4)×640 (2,4)×80 (3,6)×5280 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 640 (2,4): 80 (2,6): 8800 (3,6): 5280 (3,8): 173440 (3,10): 16960

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Two-block group-algebra code (Lin and Pryadko, arXiv:2306.16400) on G = C8:C40(r=7) of order 320, Cayley table research/kit/group_algebra.metacyclic(8, 40, 7) with the identity at index 0 and elements indexed as that builder lists them: H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] with L(g)[g h, h] = 1 and R(g)[h g, h] = 1 (research/kit/group_algebra.py build_2bga(mul, a, b)); a = [0, 13, 18, 275], b = [0, 52, 125, 302] (element indices). n = 2|G| = 640, check weight 8.
model Claude Claude Fable 5.1 (Claude Code) (claimed, not verified)
date 2026-09-26
notes Found by the fourth LER-objective search (two-block group-algebra codes over non-abelian groups with check weight 6, 7, or 8 at 420 < n <= 700 and k >= 8): circuit-level logical error rate at 3 rounds under the board's depolarizing recipe, interleaved schedule, decoded with CUDA-Q QEC nv-qldpc-decoder (BP+OSD-CS order 10). At p = 0.002, 100000 shots per basis: Z memory 0 failures, X memory 3 failures, against 20 copies of the distance-7 rotated surface code (1940 physical qubits, same builder and decoder) with 116 and 102 failures. Decoder-based d_circ estimate at 3 rounds: 52. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. Details in the accompanying note.
family other (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 8 (computed)

How this code was found

the research note submitted with this code · raw markdown · all notes

[[640,20,32]] weight-8 two-block group-algebra code on C8:C40(r=7)

Direction & hypothesis

Objective: at 3 syndrome rounds under the board's depolarizing recipe at p = 0.002, interleaved schedule, both memories, a logical error rate per round below that of k copies of the rotated surface code at equal or greater physical qubit count (data plus ancilla), with separated 95 percent Poisson intervals. The target board cell is weight-8 x unrestricted (no layout). This code comes from the non-abelian two-block group algebra, weight 6/7/8, 420 < n <= 700, k >= 8 family of the fourth LER-objective search, the ground the first three searches (two-block codes at n <= 420) did not cover; the search weighted its draws toward k >= 12, where the matched surface baseline keeps distance 7, following the third search's finding that every k >= 12 weight-7 code at 370 < n <= 420 beat its d = 7 baseline by 10 to 30x while the k = 8 codes lost to d = 9 baselines. The baseline's distance is set by the qubit budget (k20-d7: 20 copies of d = 7, 1940 qubits against the candidate's 1280), and the decoder is the same BP+OSD configuration for both.

What was searched

Stage 1 admitted 372 candidates from cyclic generalized bicycle, weight 6/7/8, 420 < n <= 700, k >= 8, 426 candidates from coprime bivariate bicycle, weight 6/7/8, 420 < n <= 700, k >= 8, 2958 candidates from non-abelian two-block group algebra, weight 6/7/8, 420 < n <= 700, k >= 8 (3,756 generator hits with the required k, connected, d >= 10 at 300 RIS trials, and no norm-lift or single-block logical below 10 for the cyclic draws; 0 repeats within the search, 0 already candidates of the first three searches, 0 exact board duplicates). Funnel: RIS at 2,000 trials (keep d >= 10; 80 of 80), RIS at 20,000 trials (80 kept), WL dedup against the board (0 dropped), 3-round circuit with the tier checks (75 built), GPU decode of 10,000 shots per basis at p = 0.002 against the matched surface baseline (11 of 11 beat it in both bases), the decoder-based d_circ estimate (4 kept, 1 more than 2 below d), then up to 100,000 shots per basis at p = 0.001 and 0.002 (fitted to a 90-minute GPU budget at the measured throughput) and a 300,000,000-trial ris_gpu pass per side.

Construction

Two-block group-algebra code (Lin and Pryadko, arXiv:2306.16400) on G = C8:C40(r=7) of order 320, Cayley table research/kit/group_algebra.metacyclic(8, 40, 7) with the identity at index 0 and elements indexed as that builder lists them: H_X = [L(a) | R(b)], H_Z = [R(b)^T | L(a)^T] with L(g)[g h, h] = 1 and R(g)[h g, h] = 1 (research/kit/group_algebra.py build_2bga(mul, a, b)); a = [0, 13, 18, 275], b = [0, 52, 125, 302] (element indices). n = 2|G| = 640, check weight 8.

Schedule: interleaved; two-block interleaved (A: 4 terms, B: 4 terms), 9 CX layers per round; terms by left/right regular terms recorded by the generator; X-check term slots [2, 7, 6, 1, 3, 5, 8, 4], Z-check term slots [6, 1, 2, 7, 4, 3, 0, 5] over terms A_0..A_3, B_0..B_3; RIS screen at 2 rounds: {'Z': 439, 'X': 433}

Evidence trail

RIS ladder for the submitted code (lightest logical found, both sides):

| RIS trials per side | seed | lightest logical found | |---|---|---| | 2,000 | 1336471719 | 88 | | 20,000 | 1196923803 | 48 | | 1,200,000 (laptop, verify/gf2_fast) | 100, 101, 102 | 32 | | 300,000,000 (GPU, verify/ris_gpu.py) | 2071533883 | X 32, Z 36 |

Claim: d <= 32, a witness-backed upper bound.

Decoder-based circuit fault-distance estimate at 3 rounds (a stacked BP+OSD search on the committed DEM, GPU, 1 seeds; our decoder-based estimator, not part of this repo): 52 (per basis {'Z': 52, 'X': 57}); an upper bound on d_circ.

Logical error rate per round at 3 rounds (exact 95 percent Poisson intervals on the failure count; the surface baseline is 20 copies of the distance-7 rotated surface code, 1940 physical qubits, geometric interleaved schedule, same noise recipe and decoder):

| p | basis | candidate | surface baseline | ratio | separated | |---|---|---|---|---|---| | 0.002 | Z | 0 [0, 4.24e-05] (0/29000) | 1.34e-03 [1.10e-03, 1.60e-03] (116/29000) | 0.000 | yes | | 0.002 | X | 3.45e-05 [7.11e-06, 1.01e-04] (3/29000) | 1.18e-03 [9.58e-04, 1.43e-03] (102/29000) | 0.029 | yes | | 0.001 | Z | 0 [0, 4.24e-05] (0/29000) | 6.90e-05 [2.53e-05, 1.50e-04] (6/29000) | 0.000 | no | | 0.001 | X | 0 [0, 4.24e-05] (0/29000) | 1.61e-04 [8.80e-05, 2.70e-04] (14/29000) | 0.000 | yes |

Stage-4 screen (10,000 shots per basis at p = 0.002): Z 0 vs 31, X 1 vs 33 failures.

Objective at p = 0.002: met (both bases separated: True).

Gate verdict (verify/validate_candidate.py, refute off): passed = True, labels: advances the weight-8 x unrestricted board; literature novelty UNVERIFIED. Duplicate check: exact None, WL None. Board cell ['weight-8', 'unrestricted']: board_advancing = True.

Dead ends

Of the candidates that reached the GPU screen, 0 did not beat their surface baseline in both bases at 10,000 shots; 1 failed the d_circ check (kept when the estimate is within 2 of d or at least 3 times the surface baseline's distance); 0 produced no deterministic schedule or failed a tier check; 0 fell below d = 10 in the RIS ladder.

Tools

Claude (Claude Code, model Fable 5.1) as the agent in an unattended search: generation and circuits on the laptop, GPU decoding on a RunPod NVIDIA A40 pod. Repo tooling: research/kit/bb.py, research/cyclic_gb.py, and research/kit/group_algebra.py (constructions), research/kit/css.py and verify/gf2_fast.cpp (k and the RIS distance screen), verify/qldpc_verify.py fingerprint and WL signature (dedup against the board), the schedule chain of PR 1859's interleaved two-block builder (research/circuit_autogen.py), a SAT coloring, and the board's sequential builder with verify/circuit_verify.py's tier checks, our decoder-based d_circ estimator (not part of this repo), a rotated-surface matched baseline built with the same interleaved builder (our own scripts, not part of this repo), CUDA-Q QEC nv-qldpc-decoder (BP min-sum 30 iterations, scale 0.625, OSD combination sweep order 10, the configuration validated against bposd-cs-10), verify/ris_gpu.py on the A40 for the deep rung, a norm-lift quotient bound and single-block kernel enumeration for the cyclic draws (our own structural bound script, not part of this repo), and verify/validate_candidate.py for the verdict.

Reproduction

import sys; sys.path.insert(0, "research/kit")
import group_algebra as ga
mul, _ = ga.metacyclic(8, 40, 7)   # Cayley table, identity at index 0
HX, HZ = ga.build_2bga(mul, [0, 13, 18, 275], [0, 52, 125, 302])   # [[640,20]]

Circuits: PR 1859's interleaved two-block builder (research/circuit_autogen.py) at 3 rounds, 9.0 CX layers per round, with the term slots listed under Construction. Decoding: strip the noise, reapply circuit_tools.apply_noise at p, derive the DEM, sample with the stim seed recorded in the receipts, decode with nv-qldpc-decoder as configured above; a failure is any logical observable decoded wrong.

Parity checks

X-checks 320 (max weight 8) · Z-checks 320 (max weight 8)
H_X (320 checks, sparse supports)
[0, 22, 27, 245, 320, 378, 475, 628] [1, 23, 28, 246, 321, 389, 556, 619] [2, 24, 29, 247, 322, 380, 477, 630] [3, 25, 30, 248, 323, 391, 558, 621] [4, 26, 31, 249, 324, 382, 479, 632] [5, 27, 32, 250, 325, 393, 520, 623] [6, 28, 33, 251, 326, 384, 441, 634] [7, 29, 34, 252, 327, 395, 522, 625] [8, 30, 35, 253, 328, 386, 443, 636] [9, 31, 36, 254, 329, 397, 524, 627] [10, 32, 37, 255, 330, 388, 445, 638] [11, 33, 38, 256, 331, 399, 526, 629] [12, 34, 39, 257, 332, 390, 447, 600] [0, 13, 35, 258, 333, 361, 528, 631] [1, 14, 36, 259, 334, 392, 449, 602] [2, 15, 37, 260, 335, 363, 530, 633] [3, 16, 38, 261, 336, 394, 451, 604] [4, 17, 39, 262, 337, 365, 532, 635] [0, 5, 18, 263, 338, 396, 453, 606] [1, 6, 19, 264, 339, 367, 534, 637] [2, 7, 20, 265, 340, 398, 455, 608] [3, 8, 21, 266, 341, 369, 536, 639] [4, 9, 22, 267, 342, 360, 457, 610] [5, 10, 23, 268, 343, 371, 538, 601] [6, 11, 24, 269, 344, 362, 459, 612] [7, 12, 25, 270, 345, 373, 540, 603] [8, 13, 26, 271, 346, 364, 461, 614] [9, 14, 27, 272, 347, 375, 542, 605] [10, 15, 28, 273, 348, 366, 463, 616] [11, 16, 29, 274, 349, 377, 544, 607] [12, 17, 30, 275, 350, 368, 465, 618] [13, 18, 31, 276, 351, 379, 546, 609] [14, 19, 32, 277, 352, 370, 467, 620] [15, 20, 33, 278, 353, 381, 548, 611] [16, 21, 34, 279, 354, 372, 469, 622] [17, 22, 35, 240, 355, 383, 550, 613] [18, 23, 36, 241, 356, 374, 471, 624] [19, 24, 37, 242, 357, 385, 552, 615] [20, 25, 38, 243, 358, 376, 473, 626] [21, 26, 39, 244, 359, 387, 554, 617] [40, 62, 205, 307, 348, 360, 418, 515] [41, 63, 206, 308, 339, 361, 429, 596] [42, 64, 207, 309, 350, 362, 420, 517] [43, 65, 208, 310, 341, 363, 431, 598] [44, 66, 209, 311, 352, 364, 422, 519] [45, 67, 210, 312, 343, 365, 433, 560] [46, 68, 211, 313, 354, 366, 424, 481] [47, 69, 212, 314, 345, 367, 435, 562] [48, 70, 213, 315, 356, 368, 426, 483] [49, 71, 214, 316, 347, 369, 437, 564] [50, 72, 215, 317, 358, 370, 428, 485] [51, 73, 216, 318, 349, 371, 439, 566] [52, 74, 217, 319, 320, 372, 430, 487] [53, 75, 218, 280, 351, 373, 401, 568] [54, 76, 219, 281, 322, 374, 432, 489] [55, 77, 220, 282, 353, 375, 403, 570] [56, 78, 221, 283, 324, 376, 434, 491] [57, 79, 222, 284, 355, 377, 405, 572] [40, 58, 223, 285, 326, 378, 436, 493] [41, 59, 224, 286, 357, 379, 407, 574] [42, 60, 225, 287, 328, 380, 438, 495] [43, 61, 226, 288, 359, 381, 409, 576] [44, 62, 227, 289, 330, 382, 400, 497] [45, 63, 228, 290, 321, 383, 411, 578] [46, 64, 229, 291, 332, 384, 402, 499] [47, 65, 230, 292, 323, 385, 413, 580] [48, 66, 231, 293, 334, 386, 404, 501] [49, 67, 232, 294, 325, 387, 415, 582] [50, 68, 233, 295, 336, 388, 406, 503] [51, 69, 234, 296, 327, 389, 417, 584] [52, 70, 235, 297, 338, 390, 408, 505] [53, 71, 236, 298, 329, 391, 419, 586] [54, 72, 237, 299, 340, 392, 410, 507] [55, 73, 238, 300, 331, 393, 421, 588] [56, 74, 239, 301, 342, 394, 412, 509] [57, 75, 200, 302, 333, 395, 423, 590] [58, 76, 201, 303, 344, 396, 414, 511] [59, 77, 202, 304, 335, 397, 425, 592] [60, 78, 203, 305, 346, 398, 416, 513] [61, 79, 204, 306, 337, 399, 427, 594] [80, 102, 165, 267, 388, 400, 458, 555] [81, 103, 166, 268, 379, 401, 469, 636] [82, 104, 167, 269, 390, 402, 460, 557] [83, 105, 168, 270, 381, 403, 471, 638] [84, 106, 169, 271, 392, 404, 462, 559] [85, 107, 170, 272, 383, 405, 473, 600] [86, 108, 171, 273, 394, 406, 464, 521] [87, 109, 172, 274, 385, 407, 475, 602] [88, 110, 173, 275, 396, 408, 466, 523] [89, 111, 174, 276, 387, 409, 477, 604] [90, 112, 175, 277, 398, 410, 468, 525] [91, 113, 176, 278, 389, 411, 479, 606] [92, 114, 177, 279, 360, 412, 470, 527] [93, 115, 178, 240, 391, 413, 441, 608] [94, 116, 179, 241, 362, 414, 472, 529] [95, 117, 180, 242, 393, 415, 443, 610] [96, 118, 181, 243, 364, 416, 474, 531] [97, 119, 182, 244, 395, 417, 445, 612] [80, 98, 183, 245, 366, 418, 476, 533] [81, 99, 184, 246, 397, 419, 447, 614] [82, 100, 185, 247, 368, 420, 478, 535] [83, 101, 186, 248, 399, 421, 449, 616] [84, 102, 187, 249, 370, 422, 440, 537] [85, 103, 188, 250, 361, 423, 451, 618] [86, 104, 189, 251, 372, 424, 442, 539] [87, 105, 190, 252, 363, 425, 453, 620] [88, 106, 191, 253, 374, 426, 444, 541] [89, 107, 192, 254, 365, 427, 455, 622] [90, 108, 193, 255, 376, 428, 446, 543] [91, 109, 194, 256, 367, 429, 457, 624] [92, 110, 195, 257, 378, 430, 448, 545] [93, 111, 196, 258, 369, 431, 459, 626] [94, 112, 197, 259, 380, 432, 450, 547] [95, 113, 198, 260, 371, 433, 461, 628] [96, 114, 199, 261, 382, 434, 452, 549] [97, 115, 160, 262, 373, 435, 463, 630] [98, 116, 161, 263, 384, 436, 454, 551] [99, 117, 162, 264, 375, 437, 465, 632] [100, 118, 163, 265, 386, 438, 456, 553] [101, 119, 164, 266, 377, 439, 467, 634] [120, 125, 142, 227, 428, 440, 498, 595] [121, 126, 143, 228, 356, 419, 441, 509] [122, 127, 144, 229, 430, 442, 500, 597] [123, 128, 145, 230, 358, 421, 443, 511] [124, 129, 146, 231, 432, 444, 502, 599] [125, 130, 147, 232, 320, 423, 445, 513] [126, 131, 148, 233, 434, 446, 504, 561] [127, 132, 149, 234, 322, 425, 447, 515] [128, 133, 150, 235, 436, 448, 506, 563] [129, 134, 151, 236, 324, 427, 449, 517] [130, 135, 152, 237, 438, 450, 508, 565] [131, 136, 153, 238, 326, 429, 451, 519] [132, 137, 154, 239, 400, 452, 510, 567] [133, 138, 155, 200, 328, 431, 453, 481] [134, 139, 156, 201, 402, 454, 512, 569] [135, 140, 157, 202, 330, 433, 455, 483] [136, 141, 158, 203, 404, 456, 514, 571] [137, 142, 159, 204, 332, 435, 457, 485] [120, 138, 143, 205, 406, 458, 516, 573] [121, 139, 144, 206, 334, 437, 459, 487] [122, 140, 145, 207, 408, 460, 518, 575] [123, 141, 146, 208, 336, 439, 461, 489] [124, 142, 147, 209, 410, 462, 480, 577] [125, 143, 148, 210, 338, 401, 463, 491] [126, 144, 149, 211, 412, 464, 482, 579] [127, 145, 150, 212, 340, 403, 465, 493] [128, 146, 151, 213, 414, 466, 484, 581] [129, 147, 152, 214, 342, 405, 467, 495] [130, 148, 153, 215, 416, 468, 486, 583] [131, 149, 154, 216, 344, 407, 469, 497] [132, 150, 155, 217, 418, 470, 488, 585] [133, 151, 156, 218, 346, 409, 471, 499] [134, 152, 157, 219, 420, 472, 490, 587] [135, 153, 158, 220, 348, 411, 473, 501] [136, 154, 159, 221, 422, 474, 492, 589] [120, 137, 155, 222, 350, 413, 475, 503] [121, 138, 156, 223, 424, 476, 494, 591] [122, 139, 157, 224, 352, 415, 477, 505] [123, 140, 158, 225, 426, 478, 496, 593] [124, 141, 159, 226, 354, 417, 479, 507] [85, 160, 182, 187, 468, 480, 538, 635] [86, 161, 183, 188, 396, 459, 481, 549] [87, 162, 184, 189, 470, 482, 540, 637] [88, 163, 185, 190, 398, 461, 483, 551] [89, 164, 186, 191, 472, 484, 542, 639] [90, 165, 187, 192, 360, 463, 485, 553] [91, 166, 188, 193, 474, 486, 544, 601] [92, 167, 189, 194, 362, 465, 487, 555] [93, 168, 190, 195, 476, 488, 546, 603] [94, 169, 191, 196, 364, 467, 489, 557] [95, 170, 192, 197, 478, 490, 548, 605] [96, 171, 193, 198, 366, 469, 491, 559] [97, 172, 194, 199, 440, 492, 550, 607] [98, 160, 173, 195, 368, 471, 493, 521] [99, 161, 174, 196, 442, 494, 552, 609] [100, 162, 175, 197, 370, 473, 495, 523] [101, 163, 176, 198, 444, 496, 554, 611] [102, 164, 177, 199, 372, 475, 497, 525] [103, 160, 165, 178, 446, 498, 556, 613] [104, 161, 166, 179, 374, 477, 499, 527] [105, 162, 167, 180, 448, 500, 558, 615] [106, 163, 168, 181, 376, 479, 501, 529] [107, 164, 169, 182, 450, 502, 520, 617] [108, 165, 170, 183, 378, 441, 503, 531] [109, 166, 171, 184, 452, 504, 522, 619] [110, 167, 172, 185, 380, 443, 505, 533] [111, 168, 173, 186, 454, 506, 524, 621] [112, 169, 174, 187, 382, 445, 507, 535] [113, 170, 175, 188, 456, 508, 526, 623] [114, 171, 176, 189, 384, 447, 509, 537] [115, 172, 177, 190, 458, 510, 528, 625] [116, 173, 178, 191, 386, 449, 511, 539] [117, 174, 179, 192, 460, 512, 530, 627] [118, 175, 180, 193, 388, 451, 513, 541] [119, 176, 181, 194, 462, 514, 532, 629] [80, 177, 182, 195, 390, 453, 515, 543] [81, 178, 183, 196, 464, 516, 534, 631] [82, 179, 184, 197, 392, 455, 517, 545] [83, 180, 185, 198, 466, 518, 536, 633] [84, 181, 186, 199, 394, 457, 519, 547] [45, 147, 200, 222, 355, 508, 520, 578] [46, 148, 201, 223, 436, 499, 521, 589] [47, 149, 202, 224, 357, 510, 522, 580] [48, 150, 203, 225, 438, 501, 523, 591] [49, 151, 204, 226, 359, 512, 524, 582] [50, 152, 205, 227, 400, 503, 525, 593] [51, 153, 206, 228, 321, 514, 526, 584] [52, 154, 207, 229, 402, 505, 527, 595] [53, 155, 208, 230, 323, 516, 528, 586] [54, 156, 209, 231, 404, 507, 529, 597] [55, 157, 210, 232, 325, 518, 530, 588] [56, 158, 211, 233, 406, 509, 531, 599] [57, 159, 212, 234, 327, 480, 532, 590] [58, 120, 213, 235, 408, 511, 533, 561] [59, 121, 214, 236, 329, 482, 534, 592] [60, 122, 215, 237, 410, 513, 535, 563] [61, 123, 216, 238, 331, 484, 536, 594] [62, 124, 217, 239, 412, 515, 537, 565] [63, 125, 200, 218, 333, 486, 538, 596] [64, 126, 201, 219, 414, 517, 539, 567] [65, 127, 202, 220, 335, 488, 540, 598] [66, 128, 203, 221, 416, 519, 541, 569] [67, 129, 204, 222, 337, 490, 542, 560] [68, 130, 205, 223, 418, 481, 543, 571] [69, 131, 206, 224, 339, 492, 544, 562] [70, 132, 207, 225, 420, 483, 545, 573] [71, 133, 208, 226, 341, 494, 546, 564] [72, 134, 209, 227, 422, 485, 547, 575] [73, 135, 210, 228, 343, 496, 548, 566] [74, 136, 211, 229, 424, 487, 549, 577] [75, 137, 212, 230, 345, 498, 550, 568] [76, 138, 213, 231, 426, 489, 551, 579] [77, 139, 214, 232, 347, 500, 552, 570] [78, 140, 215, 233, 428, 491, 553, 581] [79, 141, 216, 234, 349, 502, 554, 572] [40, 142, 217, 235, 430, 493, 555, 583] [41, 143, 218, 236, 351, 504, 556, 574] [42, 144, 219, 237, 432, 495, 557, 585] [43, 145, 220, 238, 353, 506, 558, 576] [44, 146, 221, 239, 434, 497, 559, 587] [5, 107, 240, 262, 395, 548, 560, 618] [6, 108, 241, 263, 476, 539, 561, 629] [7, 109, 242, 264, 397, 550, 562, 620] [8, 110, 243, 265, 478, 541, 563, 631] [9, 111, 244, 266, 399, 552, 564, 622] [10, 112, 245, 267, 440, 543, 565, 633] [11, 113, 246, 268, 361, 554, 566, 624] [12, 114, 247, 269, 442, 545, 567, 635] [13, 115, 248, 270, 363, 556, 568, 626] [14, 116, 249, 271, 444, 547, 569, 637] [15, 117, 250, 272, 365, 558, 570, 628] [16, 118, 251, 273, 446, 549, 571, 639] [17, 119, 252, 274, 367, 520, 572, 630] [18, 80, 253, 275, 448, 551, 573, 601] [19, 81, 254, 276, 369, 522, 574, 632] [20, 82, 255, 277, 450, 553, 575, 603] [21, 83, 256, 278, 371, 524, 576, 634] [22, 84, 257, 279, 452, 555, 577, 605] [23, 85, 240, 258, 373, 526, 578, 636] [24, 86, 241, 259, 454, 557, 579, 607] [25, 87, 242, 260, 375, 528, 580, 638] [26, 88, 243, 261, 456, 559, 581, 609] [27, 89, 244, 262, 377, 530, 582, 600] [28, 90, 245, 263, 458, 521, 583, 611] [29, 91, 246, 264, 379, 532, 584, 602] [30, 92, 247, 265, 460, 523, 585, 613] [31, 93, 248, 266, 381, 534, 586, 604] [32, 94, 249, 267, 462, 525, 587, 615] [33, 95, 250, 268, 383, 536, 588, 606] [34, 96, 251, 269, 464, 527, 589, 617] [35, 97, 252, 270, 385, 538, 590, 608] [36, 98, 253, 271, 466, 529, 591, 619] [37, 99, 254, 272, 387, 540, 592, 610] [38, 100, 255, 273, 468, 531, 593, 621] [39, 101, 256, 274, 389, 542, 594, 612] [0, 102, 257, 275, 470, 533, 595, 623] [1, 103, 258, 276, 391, 544, 596, 614] [2, 104, 259, 277, 472, 535, 597, 625] [3, 105, 260, 278, 393, 546, 598, 616] [4, 106, 261, 279, 474, 537, 599, 627] [67, 280, 285, 302, 338, 435, 588, 600] [68, 281, 286, 303, 349, 516, 579, 601] [69, 282, 287, 304, 340, 437, 590, 602] [70, 283, 288, 305, 351, 518, 581, 603] [71, 284, 289, 306, 342, 439, 592, 604] [72, 285, 290, 307, 353, 480, 583, 605] [73, 286, 291, 308, 344, 401, 594, 606] [74, 287, 292, 309, 355, 482, 585, 607] [75, 288, 293, 310, 346, 403, 596, 608] [76, 289, 294, 311, 357, 484, 587, 609] [77, 290, 295, 312, 348, 405, 598, 610] [78, 291, 296, 313, 359, 486, 589, 611] [79, 292, 297, 314, 350, 407, 560, 612] [40, 293, 298, 315, 321, 488, 591, 613] [41, 294, 299, 316, 352, 409, 562, 614] [42, 295, 300, 317, 323, 490, 593, 615] [43, 296, 301, 318, 354, 411, 564, 616] [44, 297, 302, 319, 325, 492, 595, 617] [45, 280, 298, 303, 356, 413, 566, 618] [46, 281, 299, 304, 327, 494, 597, 619] [47, 282, 300, 305, 358, 415, 568, 620] [48, 283, 301, 306, 329, 496, 599, 621] [49, 284, 302, 307, 320, 417, 570, 622] [50, 285, 303, 308, 331, 498, 561, 623] [51, 286, 304, 309, 322, 419, 572, 624] [52, 287, 305, 310, 333, 500, 563, 625] [53, 288, 306, 311, 324, 421, 574, 626] [54, 289, 307, 312, 335, 502, 565, 627] [55, 290, 308, 313, 326, 423, 576, 628] [56, 291, 309, 314, 337, 504, 567, 629] [57, 292, 310, 315, 328, 425, 578, 630] [58, 293, 311, 316, 339, 506, 569, 631] [59, 294, 312, 317, 330, 427, 580, 632] [60, 295, 313, 318, 341, 508, 571, 633] [61, 296, 314, 319, 332, 429, 582, 634] [62, 280, 297, 315, 343, 510, 573, 635] [63, 281, 298, 316, 334, 431, 584, 636] [64, 282, 299, 317, 345, 512, 575, 637] [65, 283, 300, 318, 336, 433, 586, 638] [66, 284, 301, 319, 347, 514, 577, 639]
H_Z (320 checks, sparse supports)
[0, 52, 125, 302, 320, 333, 338, 595] [1, 63, 206, 293, 321, 334, 339, 596] [2, 54, 127, 304, 322, 335, 340, 597] [3, 65, 208, 295, 323, 336, 341, 598] [4, 56, 129, 306, 324, 337, 342, 599] [5, 67, 210, 297, 325, 338, 343, 560] [6, 58, 131, 308, 326, 339, 344, 561] [7, 69, 212, 299, 327, 340, 345, 562] [8, 60, 133, 310, 328, 341, 346, 563] [9, 71, 214, 301, 329, 342, 347, 564] [10, 62, 135, 312, 330, 343, 348, 565] [11, 73, 216, 303, 331, 344, 349, 566] [12, 64, 137, 314, 332, 345, 350, 567] [13, 75, 218, 305, 333, 346, 351, 568] [14, 66, 139, 316, 334, 347, 352, 569] [15, 77, 220, 307, 335, 348, 353, 570] [16, 68, 141, 318, 336, 349, 354, 571] [17, 79, 222, 309, 337, 350, 355, 572] [18, 70, 143, 280, 338, 351, 356, 573] [19, 41, 224, 311, 339, 352, 357, 574] [20, 72, 145, 282, 340, 353, 358, 575] [21, 43, 226, 313, 341, 354, 359, 576] [22, 74, 147, 284, 320, 342, 355, 577] [23, 45, 228, 315, 321, 343, 356, 578] [24, 76, 149, 286, 322, 344, 357, 579] [25, 47, 230, 317, 323, 345, 358, 580] [26, 78, 151, 288, 324, 346, 359, 581] [27, 49, 232, 319, 320, 325, 347, 582] [28, 40, 153, 290, 321, 326, 348, 583] [29, 51, 234, 281, 322, 327, 349, 584] [30, 42, 155, 292, 323, 328, 350, 585] [31, 53, 236, 283, 324, 329, 351, 586] [32, 44, 157, 294, 325, 330, 352, 587] [33, 55, 238, 285, 326, 331, 353, 588] [34, 46, 159, 296, 327, 332, 354, 589] [35, 57, 200, 287, 328, 333, 355, 590] [36, 48, 121, 298, 329, 334, 356, 591] [37, 59, 202, 289, 330, 335, 357, 592] [38, 50, 123, 300, 331, 336, 358, 593] [39, 61, 204, 291, 332, 337, 359, 594] [22, 40, 92, 165, 360, 378, 555, 613] [13, 41, 103, 246, 361, 379, 556, 614] [24, 42, 94, 167, 362, 380, 557, 615] [15, 43, 105, 248, 363, 381, 558, 616] [26, 44, 96, 169, 364, 382, 559, 617] [17, 45, 107, 250, 365, 383, 520, 618] [28, 46, 98, 171, 366, 384, 521, 619] [19, 47, 109, 252, 367, 385, 522, 620] [30, 48, 100, 173, 368, 386, 523, 621] [21, 49, 111, 254, 369, 387, 524, 622] [32, 50, 102, 175, 370, 388, 525, 623] [23, 51, 113, 256, 371, 389, 526, 624] [34, 52, 104, 177, 372, 390, 527, 625] [25, 53, 115, 258, 373, 391, 528, 626] [36, 54, 106, 179, 374, 392, 529, 627] [27, 55, 117, 260, 375, 393, 530, 628] [38, 56, 108, 181, 376, 394, 531, 629] [29, 57, 119, 262, 377, 395, 532, 630] [0, 58, 110, 183, 378, 396, 533, 631] [31, 59, 81, 264, 379, 397, 534, 632] [2, 60, 112, 185, 380, 398, 535, 633] [33, 61, 83, 266, 381, 399, 536, 634] [4, 62, 114, 187, 360, 382, 537, 635] [35, 63, 85, 268, 361, 383, 538, 636] [6, 64, 116, 189, 362, 384, 539, 637] [37, 65, 87, 270, 363, 385, 540, 638] [8, 66, 118, 191, 364, 386, 541, 639] [39, 67, 89, 272, 365, 387, 542, 600] [10, 68, 80, 193, 366, 388, 543, 601] [1, 69, 91, 274, 367, 389, 544, 602] [12, 70, 82, 195, 368, 390, 545, 603] [3, 71, 93, 276, 369, 391, 546, 604] [14, 72, 84, 197, 370, 392, 547, 605] [5, 73, 95, 278, 371, 393, 548, 606] [16, 74, 86, 199, 372, 394, 549, 607] [7, 75, 97, 240, 373, 395, 550, 608] [18, 76, 88, 161, 374, 396, 551, 609] [9, 77, 99, 242, 375, 397, 552, 610] [20, 78, 90, 163, 376, 398, 553, 611] [11, 79, 101, 244, 377, 399, 554, 612] [62, 80, 132, 205, 400, 418, 515, 573] [53, 81, 143, 286, 401, 419, 516, 574] [64, 82, 134, 207, 402, 420, 517, 575] [55, 83, 145, 288, 403, 421, 518, 576] [66, 84, 136, 209, 404, 422, 519, 577] [57, 85, 147, 290, 405, 423, 480, 578] [68, 86, 138, 211, 406, 424, 481, 579] [59, 87, 149, 292, 407, 425, 482, 580] [70, 88, 140, 213, 408, 426, 483, 581] [61, 89, 151, 294, 409, 427, 484, 582] [72, 90, 142, 215, 410, 428, 485, 583] [63, 91, 153, 296, 411, 429, 486, 584] [74, 92, 144, 217, 412, 430, 487, 585] [65, 93, 155, 298, 413, 431, 488, 586] [76, 94, 146, 219, 414, 432, 489, 587] [67, 95, 157, 300, 415, 433, 490, 588] [78, 96, 148, 221, 416, 434, 491, 589] [69, 97, 159, 302, 417, 435, 492, 590] [40, 98, 150, 223, 418, 436, 493, 591] [71, 99, 121, 304, 419, 437, 494, 592] [42, 100, 152, 225, 420, 438, 495, 593] [73, 101, 123, 306, 421, 439, 496, 594] [44, 102, 154, 227, 400, 422, 497, 595] [75, 103, 125, 308, 401, 423, 498, 596] [46, 104, 156, 229, 402, 424, 499, 597] [77, 105, 127, 310, 403, 425, 500, 598] [48, 106, 158, 231, 404, 426, 501, 599] [79, 107, 129, 312, 405, 427, 502, 560] [50, 108, 120, 233, 406, 428, 503, 561] [41, 109, 131, 314, 407, 429, 504, 562] [52, 110, 122, 235, 408, 430, 505, 563] [43, 111, 133, 316, 409, 431, 506, 564] [54, 112, 124, 237, 410, 432, 507, 565] [45, 113, 135, 318, 411, 433, 508, 566] [56, 114, 126, 239, 412, 434, 509, 567] [47, 115, 137, 280, 413, 435, 510, 568] [58, 116, 128, 201, 414, 436, 511, 569] [49, 117, 139, 282, 415, 437, 512, 570] [60, 118, 130, 203, 416, 438, 513, 571] [51, 119, 141, 284, 417, 439, 514, 572] [102, 120, 172, 245, 440, 458, 475, 533] [6, 93, 121, 183, 441, 459, 476, 534] [104, 122, 174, 247, 442, 460, 477, 535] [8, 95, 123, 185, 443, 461, 478, 536] [106, 124, 176, 249, 444, 462, 479, 537] [10, 97, 125, 187, 440, 445, 463, 538] [108, 126, 178, 251, 441, 446, 464, 539] [12, 99, 127, 189, 442, 447, 465, 540] [110, 128, 180, 253, 443, 448, 466, 541] [14, 101, 129, 191, 444, 449, 467, 542] [112, 130, 182, 255, 445, 450, 468, 543] [16, 103, 131, 193, 446, 451, 469, 544] [114, 132, 184, 257, 447, 452, 470, 545] [18, 105, 133, 195, 448, 453, 471, 546] [116, 134, 186, 259, 449, 454, 472, 547] [20, 107, 135, 197, 450, 455, 473, 548] [118, 136, 188, 261, 451, 456, 474, 549] [22, 109, 137, 199, 452, 457, 475, 550] [80, 138, 190, 263, 453, 458, 476, 551] [24, 111, 139, 161, 454, 459, 477, 552] [82, 140, 192, 265, 455, 460, 478, 553] [26, 113, 141, 163, 456, 461, 479, 554] [84, 142, 194, 267, 440, 457, 462, 555] [28, 115, 143, 165, 441, 458, 463, 556] [86, 144, 196, 269, 442, 459, 464, 557] [30, 117, 145, 167, 443, 460, 465, 558] [88, 146, 198, 271, 444, 461, 466, 559] [32, 119, 147, 169, 445, 462, 467, 520] [90, 148, 160, 273, 446, 463, 468, 521] [34, 81, 149, 171, 447, 464, 469, 522] [92, 150, 162, 275, 448, 465, 470, 523] [36, 83, 151, 173, 449, 466, 471, 524] [94, 152, 164, 277, 450, 467, 472, 525] [38, 85, 153, 175, 451, 468, 473, 526] [96, 154, 166, 279, 452, 469, 474, 527] [0, 87, 155, 177, 453, 470, 475, 528] [98, 156, 168, 241, 454, 471, 476, 529] [2, 89, 157, 179, 455, 472, 477, 530] [100, 158, 170, 243, 456, 473, 478, 531] [4, 91, 159, 181, 457, 474, 479, 532] [142, 160, 212, 285, 435, 480, 493, 498] [46, 133, 161, 223, 436, 481, 494, 499] [144, 162, 214, 287, 437, 482, 495, 500] [48, 135, 163, 225, 438, 483, 496, 501] [146, 164, 216, 289, 439, 484, 497, 502] [50, 137, 165, 227, 400, 485, 498, 503] [148, 166, 218, 291, 401, 486, 499, 504] [52, 139, 167, 229, 402, 487, 500, 505] [150, 168, 220, 293, 403, 488, 501, 506] [54, 141, 169, 231, 404, 489, 502, 507] [152, 170, 222, 295, 405, 490, 503, 508] [56, 143, 171, 233, 406, 491, 504, 509] [154, 172, 224, 297, 407, 492, 505, 510] [58, 145, 173, 235, 408, 493, 506, 511] [156, 174, 226, 299, 409, 494, 507, 512] [60, 147, 175, 237, 410, 495, 508, 513] [158, 176, 228, 301, 411, 496, 509, 514] [62, 149, 177, 239, 412, 497, 510, 515] [120, 178, 230, 303, 413, 498, 511, 516] [64, 151, 179, 201, 414, 499, 512, 517] [122, 180, 232, 305, 415, 500, 513, 518] [66, 153, 181, 203, 416, 501, 514, 519] [124, 182, 234, 307, 417, 480, 502, 515] [68, 155, 183, 205, 418, 481, 503, 516] [126, 184, 236, 309, 419, 482, 504, 517] [70, 157, 185, 207, 420, 483, 505, 518] [128, 186, 238, 311, 421, 484, 506, 519] [72, 159, 187, 209, 422, 480, 485, 507] [130, 188, 200, 313, 423, 481, 486, 508] [74, 121, 189, 211, 424, 482, 487, 509] [132, 190, 202, 315, 425, 483, 488, 510] [76, 123, 191, 213, 426, 484, 489, 511] [134, 192, 204, 317, 427, 485, 490, 512] [78, 125, 193, 215, 428, 486, 491, 513] [136, 194, 206, 319, 429, 487, 492, 514] [40, 127, 195, 217, 430, 488, 493, 515] [138, 196, 208, 281, 431, 489, 494, 516] [42, 129, 197, 219, 432, 490, 495, 517] [140, 198, 210, 283, 433, 491, 496, 518] [44, 131, 199, 221, 434, 492, 497, 519] [5, 182, 200, 252, 395, 453, 520, 538] [86, 173, 201, 263, 396, 454, 521, 539] [7, 184, 202, 254, 397, 455, 522, 540] [88, 175, 203, 265, 398, 456, 523, 541] [9, 186, 204, 256, 399, 457, 524, 542] [90, 177, 205, 267, 360, 458, 525, 543] [11, 188, 206, 258, 361, 459, 526, 544] [92, 179, 207, 269, 362, 460, 527, 545] [13, 190, 208, 260, 363, 461, 528, 546] [94, 181, 209, 271, 364, 462, 529, 547] [15, 192, 210, 262, 365, 463, 530, 548] [96, 183, 211, 273, 366, 464, 531, 549] [17, 194, 212, 264, 367, 465, 532, 550] [98, 185, 213, 275, 368, 466, 533, 551] [19, 196, 214, 266, 369, 467, 534, 552] [100, 187, 215, 277, 370, 468, 535, 553] [21, 198, 216, 268, 371, 469, 536, 554] [102, 189, 217, 279, 372, 470, 537, 555] [23, 160, 218, 270, 373, 471, 538, 556] [104, 191, 219, 241, 374, 472, 539, 557] [25, 162, 220, 272, 375, 473, 540, 558] [106, 193, 221, 243, 376, 474, 541, 559] [27, 164, 222, 274, 377, 475, 520, 542] [108, 195, 223, 245, 378, 476, 521, 543] [29, 166, 224, 276, 379, 477, 522, 544] [110, 197, 225, 247, 380, 478, 523, 545] [31, 168, 226, 278, 381, 479, 524, 546] [112, 199, 227, 249, 382, 440, 525, 547] [33, 170, 228, 240, 383, 441, 526, 548] [114, 161, 229, 251, 384, 442, 527, 549] [35, 172, 230, 242, 385, 443, 528, 550] [116, 163, 231, 253, 386, 444, 529, 551] [37, 174, 232, 244, 387, 445, 530, 552] [118, 165, 233, 255, 388, 446, 531, 553] [39, 176, 234, 246, 389, 447, 532, 554] [80, 167, 235, 257, 390, 448, 533, 555] [1, 178, 236, 248, 391, 449, 534, 556] [82, 169, 237, 259, 392, 450, 535, 557] [3, 180, 238, 250, 393, 451, 536, 558] [84, 171, 239, 261, 394, 452, 537, 559] [45, 222, 240, 292, 355, 413, 560, 578] [126, 213, 241, 303, 356, 414, 561, 579] [47, 224, 242, 294, 357, 415, 562, 580] [128, 215, 243, 305, 358, 416, 563, 581] [49, 226, 244, 296, 359, 417, 564, 582] [130, 217, 245, 307, 320, 418, 565, 583] [51, 228, 246, 298, 321, 419, 566, 584] [132, 219, 247, 309, 322, 420, 567, 585] [53, 230, 248, 300, 323, 421, 568, 586] [134, 221, 249, 311, 324, 422, 569, 587] [55, 232, 250, 302, 325, 423, 570, 588] [136, 223, 251, 313, 326, 424, 571, 589] [57, 234, 252, 304, 327, 425, 572, 590] [138, 225, 253, 315, 328, 426, 573, 591] [59, 236, 254, 306, 329, 427, 574, 592] [140, 227, 255, 317, 330, 428, 575, 593] [61, 238, 256, 308, 331, 429, 576, 594] [142, 229, 257, 319, 332, 430, 577, 595] [63, 200, 258, 310, 333, 431, 578, 596] [144, 231, 259, 281, 334, 432, 579, 597] [65, 202, 260, 312, 335, 433, 580, 598] [146, 233, 261, 283, 336, 434, 581, 599] [67, 204, 262, 314, 337, 435, 560, 582] [148, 235, 263, 285, 338, 436, 561, 583] [69, 206, 264, 316, 339, 437, 562, 584] [150, 237, 265, 287, 340, 438, 563, 585] [71, 208, 266, 318, 341, 439, 564, 586] [152, 239, 267, 289, 342, 400, 565, 587] [73, 210, 268, 280, 343, 401, 566, 588] [154, 201, 269, 291, 344, 402, 567, 589] [75, 212, 270, 282, 345, 403, 568, 590] [156, 203, 271, 293, 346, 404, 569, 591] [77, 214, 272, 284, 347, 405, 570, 592] [158, 205, 273, 295, 348, 406, 571, 593] [79, 216, 274, 286, 349, 407, 572, 594] [120, 207, 275, 297, 350, 408, 573, 595] [41, 218, 276, 288, 351, 409, 574, 596] [122, 209, 277, 299, 352, 410, 575, 597] [43, 220, 278, 290, 353, 411, 576, 598] [124, 211, 279, 301, 354, 412, 577, 599] [12, 85, 262, 280, 373, 600, 618, 635] [23, 166, 253, 281, 374, 601, 619, 636] [14, 87, 264, 282, 375, 602, 620, 637] [25, 168, 255, 283, 376, 603, 621, 638] [16, 89, 266, 284, 377, 604, 622, 639] [27, 170, 257, 285, 378, 600, 605, 623] [18, 91, 268, 286, 379, 601, 606, 624] [29, 172, 259, 287, 380, 602, 607, 625] [20, 93, 270, 288, 381, 603, 608, 626] [31, 174, 261, 289, 382, 604, 609, 627] [22, 95, 272, 290, 383, 605, 610, 628] [33, 176, 263, 291, 384, 606, 611, 629] [24, 97, 274, 292, 385, 607, 612, 630] [35, 178, 265, 293, 386, 608, 613, 631] [26, 99, 276, 294, 387, 609, 614, 632] [37, 180, 267, 295, 388, 610, 615, 633] [28, 101, 278, 296, 389, 611, 616, 634] [39, 182, 269, 297, 390, 612, 617, 635] [30, 103, 240, 298, 391, 613, 618, 636] [1, 184, 271, 299, 392, 614, 619, 637] [32, 105, 242, 300, 393, 615, 620, 638] [3, 186, 273, 301, 394, 616, 621, 639] [34, 107, 244, 302, 395, 600, 617, 622] [5, 188, 275, 303, 396, 601, 618, 623] [36, 109, 246, 304, 397, 602, 619, 624] [7, 190, 277, 305, 398, 603, 620, 625] [38, 111, 248, 306, 399, 604, 621, 626] [9, 192, 279, 307, 360, 605, 622, 627] [0, 113, 250, 308, 361, 606, 623, 628] [11, 194, 241, 309, 362, 607, 624, 629] [2, 115, 252, 310, 363, 608, 625, 630] [13, 196, 243, 311, 364, 609, 626, 631] [4, 117, 254, 312, 365, 610, 627, 632] [15, 198, 245, 313, 366, 611, 628, 633] [6, 119, 256, 314, 367, 612, 629, 634] [17, 160, 247, 315, 368, 613, 630, 635] [8, 81, 258, 316, 369, 614, 631, 636] [19, 162, 249, 317, 370, 615, 632, 637] [10, 83, 260, 318, 371, 616, 633, 638] [21, 164, 251, 319, 372, 617, 634, 639]
Code ID 640-20-32 · download JSON · raw on GitHub