← back to the board
[[534,24,28]] d ≤
n
534
k
24
d
28
kd²/n
35.236
w
8
X/Z
1

Share this result

Distance

X/Z asymmetry 1 · d_X ≤ 28, d_Z ≤ 28 · 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 28 · witness weight 28 (claimed upper_bound)
witness found by @vprusso · verify/ris_gpu.py (build/ris_gpu, NVIDIA A40) · found at 2×104 trials · survived 10×108 trials · 2026-09-26
witness operator (support, 28 qubits)
[4, 23, 42, 44, 61, 63, 65, 82, 84, 103, 105, 168, 187, 208, 250, 277, 280, 283, 289, 292, 301, 304, 307, 424, 427, 430, 436, 529]
d_Z 28 · witness weight 28 (claimed upper_bound)
witness found by @vprusso · verify/ris_gpu.py (build/ris_gpu, NVIDIA A40) · found at 1.7×108 trials · survived 10×108 trials · 2026-09-26
witness operator (support, 28 qubits)
[44, 47, 50, 59, 62, 68, 71, 74, 89, 182, 188, 191, 194, 267, 269, 286, 288, 290, 307, 309, 328, 347, 368, 410, 431, 450, 513, 515]
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 6 · H_Z 6 (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)×534 (2,6)×7476 (3,6)×3738 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,4): 534 (2,6): 7476 (3,6): 3738 (3,8): 145782 (3,10): 14952
trapping sets H_Z (1,4)×534 (2,6)×7476 (3,6)×3738 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,4): 534 (2,6): 7476 (3,6): 3738 (3,8): 145782 (3,10): 14952

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction Cyclic generalized-bicycle code over Z_267 (n = 2m = 534): a(x) = 1 + x129 + x249 + x264, b(x) = 1 + x164 + x183 + x246; H_X = [circ(a)|circ(b)], H_Z = [circ(b)^T|circ(a)^T], where circ(v) has first row v and row i = v rolled by i (research/cyclic_gb.py build_cyclic_gb(267, a, b) with a, b the 0/1 first rows). k = 2 deg gcd(a, b, x267 + 1).
model Claude Claude Fable 5.1 (Claude Code) (claimed, not verified)
date 2026-09-26
notes Found by the fourth LER-objective search (cyclic generalized-bicycle codes 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 16 failures, X memory 16 failures, against 24 copies of the distance-5 rotated surface code (1176 physical qubits, same builder and decoder) with 1095 and 1116 failures. Decoder-based d_circ estimate at 3 rounds: 34. Distance: RIS at 20,000 trials (gf2_fast) and a 300,000,000-trial verify/ris_gpu.py pass per side; upper bounds. A norm-lift quotient bound over the divisors of m and a single-block kernel bound were run before admission (lightest lift 39). 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

[[534,24,28]] weight-8 cyclic generalized-bicycle code on Z_267

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 cyclic generalized bicycle, 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 (k24-d5: 24 copies of d = 5, 1176 qubits against the candidate's 1068), 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 (29 of 29 beat it in both bases), the decoder-based d_circ estimate (28 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

Cyclic generalized-bicycle code over Z_267 (n = 2m = 534): a(x) = 1 + x^129 + x^249 + x^264, b(x) = 1 + x^164 + x^183 + x^246; H_X = [circ(a)|circ(b)], H_Z = [circ(b)^T|circ(a)^T], where circ(v) has first row v and row i = v rolled by i (research/cyclic_gb.py build_cyclic_gb(267, a, b) with a, b the 0/1 first rows). k = 2 deg gcd(a, b, x^267 + 1).

Schedule: interleaved; two-block interleaved (A: 4 terms, B: 4 terms), 9 CX layers per round; terms by bb_decompose translations on Z_1 x Z_267; 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': 362, 'X': 356}

Evidence trail

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

| RIS trials per side | seed | lightest logical found | |---|---|---| | 2,000 | 1357118832 | 33 | | 20,000 | 1928504117 | 33 | | 200,000 (laptop, verify/gf2_fast) | 26510436 | 28 | | 999,999,996 (GPU, verify/ris_gpu.py) | 755471799 | X 28, Z 28 | | 999,999,996 (GPU, verify/ris_gpu.py, second independent pass, own seeds) | c59c3de45403 | X 28, Z 28 |

Claim: d <= 28, 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): 34 (per basis {'Z': 107, 'X': 34}); 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 24 copies of the distance-5 rotated surface code, 1176 physical qubits, geometric interleaved schedule, same noise recipe and decoder):

| p | basis | candidate | surface baseline | ratio | separated | |---|---|---|---|---|---| | 0.002 | Z | 1.24e-04 [7.09e-05, 2.01e-04] (16/43000) | 8.64e-03 [8.12e-03, 9.17e-03] (1095/43000) | 0.014 | yes | | 0.002 | X | 1.24e-04 [7.09e-05, 2.01e-04] (16/43000) | 8.81e-03 [8.29e-03, 9.35e-03] (1116/43000) | 0.014 | yes | | 0.001 | Z | 0 [0, 2.86e-05] (0/43000) | 1.22e-03 [1.04e-03, 1.43e-03] (157/43000) | 0.000 | yes | | 0.001 | X | 0 [0, 2.86e-05] (0/43000) | 1.15e-03 [9.72e-04, 1.35e-03] (148/43000) | 0.000 | yes |

Stage-4 screen (10,000 shots per basis at p = 0.002): Z 3 vs 255, X 7 vs 258 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")
from cyclic_gb import build_cyclic_gb
m = 267; a = [0] * m; b = [0] * m
for e in [0, 129, 249, 264]: a[e] = 1
for e in [0, 164, 183, 246]: b[e] = 1
HX, HZ = build_cyclic_gb(m, a, b)   # [[534,24]]

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