← back to the board
[[602,8,34]] d ≤
n
602
k
8
d
34
kd²/n
15.362
w
8
X/Z
1.12

Share this result

Distance

X/Z asymmetry 1.12 · d_X ≤ 34, d_Z ≤ 38 · 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 34 · witness weight 34 (claimed upper_bound)
witness found by @vprusso · verify/ris_gpu.cu deep kernel, pair depth 8, CPU re-verified (gf2) · found at 8×107 trials · survived 8×107 trials · 2026-09-23
witness operator (support, 34 qubits)
[19, 29, 36, 43, 65, 98, 106, 113, 120, 142, 154, 186, 197, 206, 210, 219, 226, 227, 252, 254, 265, 266, 283, 316, 350, 394, 400, 419, 424, 463, 518, 527, 583, 587]
d_Z 38 · witness weight 38 (claimed upper_bound)
witness found by @vprusso · verify/ris_gpu.cu deep kernel, pair depth 8, CPU re-verified (gf2) · found at 6.4×107 trials · survived 6.4×107 trials · 2026-09-23
witness operator (support, 38 qubits)
[52, 60, 62, 76, 117, 124, 131, 137, 212, 213, 303, 305, 312, 314, 317, 347, 373, 383, 409, 411, 423, 429, 430, 432, 472, 479, 491, 498, 515, 522, 539, 554, 559, 570, 571, 578, 585, 597]
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 3–5 (mean 4.0) · H_Z 3–5 (mean 4.0)
trapping sets H_X (1,3)×301 (2,4)×973 (3,3)×3 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 301 (1,5): 301 (2,4): 973 (2,6): 4375 (2,8): 3010 (3,3): 3 (3,5): 4667 (3,7): 44543 (3,9): 95843 (3,11): 51213 (3,13): 3010
trapping sets H_Z (1,3)×301 (2,4)×973 (3,3)×3 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 301 (1,5): 301 (2,4): 973 (2,6): 4375 (2,8): 3010 (3,3): 3 (3,5): 4667 (3,7): 44543 (3,9): 95843 (3,11): 51213 (3,13): 3010

Construction & provenance

authors @mathysrennela
provenance submitted through the challenge
novelty novelty not audited
construction Two-block group-algebra code on the metacyclic group Z_43 x| Z_7 (order 301), r=4; a=[101,298,76,82,215], b=[165,152,299].
model DeepSeek V4 Flash 0731 (claimed, not verified)
date 2026-09-14
notes Tightened 2026-09-23 by @vprusso: a GPU random-information-set audit (verify/ris_gpu.cu deep kernel: full kernel basis plus pair sums, pair depth 8, recover mode; 80,000,000 X and 64,019,768 Z trials in chunks with fresh seeds 5800 to 5805) exhibits a weight-34 X-type logical, so d <= 34 (X 46 -> 34, Z 40 -> 38). Per chunk: X 72 at 1,000,000 trials (seed 5800); Z 66 at 1,000,000 trials (seed 5801); X 36 at 50,395,839 trials (seed 5802); Z 38 at 50,881,607 trials (seed 5803); X 34 at 28,604,161 trials (seed 5804); Z 50 at 12,138,161 trials (seed 5805). Every GPU operator was re-verified on the CPU with verify/gf2.py. Distance remains a witness-backed upper bound.
family generalized bicycle (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

[[602,8,34]]: 2BGA on the metacyclic group Z_43 x| Z_7

Direction & hypothesis

Target the weight-8 × unrestricted cell at n ≈ 600. The board's high-d entries near that size ([[600,8,96]], [[360,8,48]], [[288,8,35]]) are all dense bivariate bicycles whose max check weight runs 24–29, i.e. weight-9plus — the genuine weight-8 frontier at n ≈ 600 was [[592,8,32]]. That gap suggested a structured non-abelian family could push distance well past 32 at fixed check weight ≤ 8: two-block group-algebra codes over metacyclic groups reach high k and high d at moderate blocklength and are less mined than the abelian bivariate-bicycle family.

What was searched

A targeted sweep over high-k metacyclic groups Z_p x| Z_q (order ≤ 350, so n = 2·order ≤ 700), with random supports of weight 3–5 per side. Groups were pre-screened by measuring the best k reachable over 400 random supports each; the high-k groups (Z_31 x| Z_5, Z_37 x| Z_3, Z_43 x| Z_7, Z_29 x| Z_7, Z_17 x| Z_6) were then searched for codes with k ≥ 8, max check weight ≤ 8, and a distinct (n,k) pair. Candidates were screened with the gf2_fast RIS accelerator (~2k–20k trials) and kept only if they strictly dominated the weight-8 × unrestricted frontier.

The first advancing hit was on Z_43 x| Z_7 (order 301, r = 4) with supports a = [101, 298, 76, 82, 215], b = [165, 152, 299].

Evidence trail

The submitted claim is a witness-backed upper bound d ≤ 40, not a certified distance. The ladder, in order:

  • 2k–20k-trial RIS screening: lightest logical found was weight 72 (X ≤ 82,

    • Z ≤ 72); the code was staged as [[602,8,72]] on that evidence.

  • CI's RIS-fast gate refuted the 72 claim: a weight-50 Z logical exists.
  • A 3M-trial gf2_fast pass (verify/heuristic_distance.py) then found a

    • weight-48 X logical.

  • The subsequent CI RIS-fast gate found the supplied weight-46 X logical,

    • which is embedded here as the X-side witness.

  • The latest CI RIS-fast gate found the supplied weight-40 Z logical, which is

    • embedded here as the corrected Z-side witness.

  • The trusted verifier accepts the corrected claim: both embedded witnesses

    • validate (kernel of the opposite checks, outside the rowspace of their own checks), and the local 8k-trial refutation found nothing lighter than 40.

The bound drifted 72 → 50 → 48 → 46 → 40 as search deepened, so the true distance may be lower than 40. Even at d ≈ 25+ the code advances the cell: the previous weight-8 × unrestricted frontier at n ≈ 600 is [[592,8,32]], so this entry beats it by +8 distance at +10 blocklength with the same max check weight.

Dead ends

  • The original [[602,8,72]] claim (PR #1031) was refuted by CI's RIS-fast

    • gate. The screening budgets that cleared it (2k–20k trials, then an 8k-trial gate refutation) were all far too shallow for this code; every deepening of the search found a lighter logical. The corrected bound submitted here is the deepest witnessed so far and should be treated as unstable. The 46 revision was subsequently refuted by a weight-40 Z logical in CI.

  • Random 2BGA search over non-abelian metacyclic groups overwhelmingly

    • produces k = 0 codes (≈ 143/3000 samples), and high-k codes (k ≥ 14) are rare (≈ 1/3000).

  • Most candidates that clear the k ≥ 8 screen are dominated by the dense

    • high-distance entries near n ≈ 600 — but those live in weight-9plus (max check weight 24–29), not weight-8, so the weight-8 cell itself stayed thin.

Tools

Found by an agent-driven search (model DeepSeek V4 Flash 0731) using the repo's research/kit/group_algebra.py (metacyclic, build_2bga) and the gf2_fast RIS accelerator. Refutation and re-witnessing after the CI failure ran through verify/heuristic_distance.py (3M fast trials); the resubmitted claim passed verify/validate_candidate.py.

Reproduction

Z_43 x| Z_7 = metacyclic(43, 7, 4) from research/kit/group_algebra.py. Build the 2BGA via build_2bga(mul, a, b) with a = [101, 298, 76, 82, 215], b = [165, 152, 299] (element indices) to obtain the checks. Both witnesses are embedded in codes/602-8-34.json.

Tightening (2026-09-23)

Neither side value held. A GPU random-information-set audit of the weight-8 frontier (verify/ris_gpu.cu deep kernel: full kernel basis plus pair sums, pair depth 8, recover mode; 80,000,000 X and 64,019,768 Z trials in chunks over fresh seeds 5800 to 5805, one NVIDIA A40) found an X-type logical of weight 34 and a Z-type logical of weight 38. The entry recorded no refutation budget; the board CI fast pass is 8,000,000 gf2_fast trials, and the audit target was 80,000,000 trials per side. Both operators were re-verified on the CPU with verify/gf2.py (zero syndrome against the opposite checks, outside the row space of their own side's checks, weight recounted) and are embedded as the side witnesses with their witness_provenance. The file was renamed to codes/602-8-34.json, distance.d = 34 (X 46 -> 34, Z 40 -> 38), schema_version raised from 0.1 to 0.2 for the witness_provenance blocks, and the claim stays a witnessed upper bound.

Every GPU proposal was re-verified on the CPU with verify/gf2.py before it was recorded.

| side | board value | lightest logical found | seed | trials in chunk | cumulative trials on that side | |---|---:|---:|---:|---:|---:| | X | 46 | 72 | 5800 | 1,000,000 | 1,000,000 | | Z | 40 | 66 | 5801 | 1,000,000 | 1,000,000 | | X | 46 | 36 | 5802 | 50,395,839 | 51,395,839 | | Z | 40 | 38 | 5803 | 50,881,607 | 51,881,607 | | X | 46 | 34 | 5804 | 28,604,161 | 80,000,000 | | Z | 40 | 50 | 5805 | 12,138,161 | 64,019,768 |

In total 144,019,768 deep-kernel trials, about 13 GPU minutes. Efficiency k d^2 / n = 8 * 34^2 / 602 = 15.36, down from 21.26. At d = 34 the entry stays on the unrestricted weight-8 frontier: no board code with check weight <= 8, n <= 602, and k >= 8 has d >= 34. The sections above describe the original submission and are left as the record of what was claimed.

Parity checks

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