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[[712,182,20]] d ≤
n
712
k
182
d
20
kd²/n
102.247
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 20, d_Z ≤ 20 · 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 20 · witness weight 20 (claimed upper_bound)
witness found by @vprusso · GPU deep kernel (full basis, pair depth 8), screen stage 3 · found at 107 trials · survived 7×107 trials · 2026-09-25
witness operator (support, 20 qubits)
[35, 44, 63, 87, 93, 94, 154, 191, 200, 219, 254, 262, 276, 284, 346, 419, 450, 520, 521, 563]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness found by @vprusso · GPU deep kernel (full basis, pair depth 8), screen stage 3 · found at 107 trials · survived 7×107 trials · 2026-09-25
witness operator (support, 20 qubits)
[9, 18, 36, 65, 142, 146, 203, 250, 319, 342, 349, 435, 441, 471, 475, 565, 605, 617, 673, 697]
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 8 · H_Z 8 (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 · H_Z 3
trapping sets H_X (1,3)×712 (2,4)×7476 (3,5)×104664 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 712 (2,4): 7476 (3,5): 104664 (3,7): 14952
trapping sets H_Z (1,3)×712 (2,4)×7476 (3,5)×104664 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 712 (2,4): 7476 (3,5): 104664 (3,7): 14952

Construction & provenance

authors @vprusso
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), prime lift P=89, n=8P=712, k=2P+4=182. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_89: E_x = [[74, 57, 77, 8, 35, 1, 19, 42], [48, 0, 70, 14, 10, 18, 13, 63], [64, 42, 75, 47, 10, 59, 2, 8]], E_z = [[67, 8, 78, 32, 28, 25, 20, 82], [0, 59, 3, 88, 51, 3, 35, 33], [87, 0, 20, 6, 33, 18, 36, 55]]. The arrays solve the joint design system E_x[i][j] - E_x[i][j'] - E_z[i'][j] + E_z[i'][j'] = 0 for each column pair of the matching M[(i-i') mod 3], M0=(0,4)(1,7)(2,6)(3,5), M1=(0,7)(1,2)(3,4)(5,6), M2=(0,2)(1,5)(3,7)(4,6); girth 8 (no 4- or 6-cycles in either exponent array); the solution was hill-climbed in the 19-dimensional null space of the design system to reduce the number of 8-cycles of the two lifted Tanner graphs (1264 -> 992 pattern solutions over 2000 single-coordinate moves). Same construction and design system as the board's [[776,198,20]] (P = 97), [[808,206,20]] (P = 101), [[664,170,18]] (P = 83), [[632,162,18]] (P = 79), and [[584,150,18]] (P = 73).
model Claude Claude Fable 5.1 (Claude Code) (claimed, not verified)
builds on arXiv:2607.14091, arXiv:2111.03654
date 2026-09-25
notes Found by a GPU random-information-set screen (verify/ris_gpu.cu deep kernel: full-basis RREF plus pair sums) over hill-climbed pair-partition CPM (3,8) draws at prime lifts P in {89, 97, 101, 103, 107, 109, 113}; see the research note for the ladder and the search tables. Lightest logicals: X 20, Z 20. Deep-kernel GPU passes: screen stages 300,000 / 2,000,000 / 10,000,000 trials per side, then 50,000,000 (X, seed 777) and 50,000,000 (Z, seed 778) deep-kernel trials reading 20 and 20; board fast pass (8,000,000 gf2_fast trials, pair depth 8) read 20 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound; every logical of this family has even weight (the all-ones vector is the sum of the rows of each check matrix). Novelty: no isomorphic code found by a nauty canonical-form check against the board and the 2BGA, GB, BB, QECDB, and codetables data (submitter claim). Generator spec: {"family": "cpm38", "P": 89, "E": [[74, 57, 77, 8, 35, 1, 19, 42], [48, 0, 70, 14, 10, 18, 13, 63], [64, 42, 75, 47, 10, 59, 2, 8]], "D": [[67, 8, 78, 32, 28, 25, 20, 82], [0, 59, 3, 88, 51, 3, 35, 33], [87, 0, 20, 6, 33, 18, 36, 55]]}
family pair-partition CPM (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

[[712,182,20]] pair-partition CPM (3,8) code at prime lift P = 89

Direction & hypothesis

Cell: unrestricted x weight-8, extended tier (n in (700, 1000], w <= 8, d <= 40). The cell's high-rate end is the pair-partition CPM family of arXiv:2607.14091: [[776,198,20]] at P = 97 (kd^2/n = 102.06) and [[808,206,20]] at P = 101 (101.98). In this family n = 8P and k = 2P + 4, so the score is d^2 (1/4 + 1/(2P)). Two facts shaped the search: every column of H_X and of H_Z has weight 3, so the all-ones vector is the sum of the rows of each matrix and every logical operator has even weight (d = 21 cannot occur, the next value above 20 is 22); and among the six isomorphism classes of disjoint matching triples for the (3,8) design system only the paper's (the cube 1-factorization, nullity 19) admits girth-8 solutions, so there is no alternative design to draw from. The 2026-09-23 stream of 2,700 random girth-8 draws at P = 89 to 113 reached 20 and never 22, so random draws were replaced by draws hill-climbed on the 8-cycle count of the exponent arrays. A d = 20 member at P = 89 scores 102.25, above both incumbents; the random stream had 258 draws at P = 89 with none above 18.

What was searched

  • Design system of arXiv:2607.14091 over F_P (36 equations in 48 unknowns,

    • nullity 19); random null-space vectors give the exponent arrays E_x, E_z; draws with a 4- or 6-cycle in either array are discarded. Each accepted draw was then hill-climbed for 1,000 or 2,000 single-coordinate moves in the null space, rejecting moves that break girth 8 and accepting moves that do not increase the number of 8-cycle pattern solutions of E_x plus E_z (closed non-backtracking walks of length 8 on the 3 x 8 base graph with vanishing alternating exponent sum). The mean count fell from about 1,230 to about 960 per draw.

  • Screen: verify/ris_gpu.cu's deep kernel (full-basis RREF plus pair sums,

    • pair depth 8), three stages per side of 300,000, 2,000,000, and 10,000,000 trials, early stop as soon as a logical lighter than the record threshold appears (20 at P = 89, 21 from P = 97 on; equal parameters count as dominated).

  • 5604 climbed draws over two NVIDIA A40s on 2026-09-25 (P drawn with

    • weights 89: 0.60, 97: 0.05, 101 to 113: 0.07 each in the pre-generated stream; uniform in the first in-process stream):

| P | n | draws | lightest logical found per draw (deep-kernel screen, early stop below the threshold) | |---:|---:|---:|---| | 89 | 712 | 3311 | 8: 1, 10: 5, 12: 80, 14: 401, 16: 1843, 18: 965, 20: 16 | | 97 | 776 | 293 | 12: 3, 14: 20, 16: 113, 18: 121, 20: 36 | | 101 | 808 | 391 | 10: 1, 12: 2, 14: 19, 16: 129, 18: 160, 20: 80 | | 103 | 824 | 410 | 10: 1, 12: 4, 14: 16, 16: 145, 18: 156, 20: 88 | | 107 | 856 | 391 | 12: 3, 14: 16, 16: 141, 18: 125, 20: 106 | | 109 | 872 | 411 | 12: 1, 14: 9, 16: 122, 18: 138, 20: 141 | | 113 | 904 | 397 | 12: 1, 14: 10, 16: 101, 18: 102, 20: 181, 22: 2 |

Evidence trail

Every operator was re-verified on the CPU with verify/gf2.py (zero syndrome against the opposite checks, outside the row space of its own checks, weight recounted) before it was recorded.

| instrument | side | trials | seed | lightest logical | |---|---|---:|---:|---:| | screen stage 1, GPU deep kernel (full basis, pair depth 8) | X | 300,000 | 83000018011 | 20 | | screen stage 2, GPU deep kernel (full basis, pair depth 8) | X | 2,000,000 | 83000018300 | 20 | | screen stage 3, GPU deep kernel (full basis, pair depth 8) (recover) | X | 10,000,000 | 83000018600 | 20 | | finalist GPU deep kernel (full basis, pair depth 8) | X | 50,000,000 | 777 | 20 | | screen stage 1, GPU deep kernel (full basis, pair depth 8) | Z | 300,000 | 83000018012 | 20 | | screen stage 2, GPU deep kernel (full basis, pair depth 8) | Z | 2,000,000 | 83000018301 | 20 | | screen stage 3, GPU deep kernel (full basis, pair depth 8) (recover) | Z | 10,000,000 | 83000018601 | 20 | | finalist GPU deep kernel (full basis, pair depth 8) | Z | 50,000,000 | 778 | 20 | | board fast pass, gf2_fast pair depth 8, 2 threads, both sides | both | 8,000,000 | 2509 | 20 |

Board CPU gate (verify/validate_candidate.py, then verify/gate_changed.py's structural and fast passes, run out of CI on the candidate file):

  • validate_candidate passed = True (its 8000-trial pure-Python refute_check found nothing lighter); structural pass: not a circulant GB, zero trials; gf2_fast fast pass: lightest logical 20 at 8,000,000 trials (9292 s, 2 threads); verdict passed.

Claim: witness-backed upper bound d <= 20 (X <= 20, Z <= 20), not exact. Both sides read 20 at every rung from 300,000 to the deepest pass, and the parity of the family means the bound cannot be off by one.

Dead ends

  • Random girth-8 draws on 2026-09-23: 258 at P = 89 with lightest logicals

    • 6 to 18 and none at 20; 441 at P = 113 with none above 20. The hill-climbed draws of this run reached 20 at P = 89 in 16 of 3311 draws and 22 at P = 113 in 2 of 397.

  • d = 20 draws at P = 97 recur under the climb (they tie [[776,198,20]] and

    • are not records) and d = 20 at P = 101 to 113 recurs (101.8 to 101.9, below the P = 101 entry); nothing reached 22 at any lift.

  • Weight-8 variants of the non-abelian lifted products of arXiv:2607.28795

    • and arXiv:2607.27644 (entry weights (3,2)/(3,2), |G| = 140 to 200): the classical distance of the (3,2) seed rows never exceeded 15 over 87,600 seeds on 236 groups, and the quantum distance of a one-row lifted product does not exceed its seed distances; no product reached 19.

  • Two-block group-algebra codes with k >= 150 at n = 700 to 1000: reachable

    • only through weight-4 elements with 75-dimensional annihilators, and every such pair had d <= 5.

Tools

verify/ris_gpu.cu (deep kernel) built with nvcc for an NVIDIA A40, driven through verify/ris_gpu.py's input format; gf2_fast from verify/ for exact k and kernels; verify/validate_candidate.py and verify/gate_changed.py for the gate; the design-system solver, girth filter, 8-cycle counter, and hill climb are a few dozen lines of Python (Gaussian elimination over F_P, cycle enumeration over the 3 x 8 arrays), described in full above. Model: Claude Fable 5.1 (Claude Code). About 16 GPU-hours over the two pods for the whole run, of which this code's own passes took under two.

Reproduction

Rebuild (H_X, H_Z) from the construction string in the code file's provenance: Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), prime lift P=89, n=8P=712, k=2P+4=182. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_89: E_x = [[74, 57, 77, 8, 35, 1, 19, 42], [48, 0, 70, 14, 10, 18, 13, 63], [64, 42, 75, 47, 10, 59, 2, 8]], E_z = [[67, 8, 78, 32, 28, 25, 20, 82], [0, 59, 3, 88, 51, 3, 35, 33], [87, 0, 20, 6, 33, 18, 36, 55]]. The arrays solve the joint design system E_x[i][j] - E_x[i][j'] - E_z[i'][j] + E_z[i'][j'] = 0 for each column pair of the matching M[(i-i') mod 3], M0=(0,4)(1,7)(2,6)(3,5), M1=(0,7)(1,2)(3,4)(5,6), M2=(0,2)(1,5)(3,7)(4,6); girth 8 (no 4- or 6-cycles in either exponent array); the solution was hill-climbed in the 19-dimensional null space of the design system to reduce the number of 8-cycles of the two lifted Tanner graphs (1264 -> 992 pattern solutions over 2000 single-coordinate moves). Same construction and design system as the board's [[776,198,20]] (P = 97), [[808,206,20]] (P = 101), [[664,170,18]] (P = 83), [[632,162,18]] (P = 79), and [[584,150,18]] (P = 73).

Parity checks

X-checks 267 (max weight 8) · Z-checks 267 (max weight 8)
H_X (267 checks, sparse supports)
[15, 121, 190, 348, 410, 533, 604, 670] [16, 122, 191, 349, 411, 445, 605, 671] [17, 123, 192, 350, 412, 446, 606, 672] [18, 124, 193, 351, 413, 447, 607, 673] [19, 125, 194, 352, 414, 448, 608, 674] [20, 126, 195, 353, 415, 449, 609, 675] [21, 127, 196, 354, 416, 450, 610, 676] [22, 128, 197, 355, 417, 451, 611, 677] [23, 129, 198, 267, 418, 452, 612, 678] [24, 130, 199, 268, 419, 453, 613, 679] [25, 131, 200, 269, 420, 454, 614, 680] [26, 132, 201, 270, 421, 455, 615, 681] [27, 133, 202, 271, 422, 456, 616, 682] [28, 134, 203, 272, 423, 457, 617, 683] [29, 135, 204, 273, 424, 458, 618, 684] [30, 136, 205, 274, 425, 459, 619, 685] [31, 137, 206, 275, 426, 460, 620, 686] [32, 138, 207, 276, 427, 461, 621, 687] [33, 139, 208, 277, 428, 462, 622, 688] [34, 140, 209, 278, 429, 463, 534, 689] [35, 141, 210, 279, 430, 464, 535, 690] [36, 142, 211, 280, 431, 465, 536, 691] [37, 143, 212, 281, 432, 466, 537, 692] [38, 144, 213, 282, 433, 467, 538, 693] [39, 145, 214, 283, 434, 468, 539, 694] [40, 146, 215, 284, 435, 469, 540, 695] [41, 147, 216, 285, 436, 470, 541, 696] [42, 148, 217, 286, 437, 471, 542, 697] [43, 149, 218, 287, 438, 472, 543, 698] [44, 150, 219, 288, 439, 473, 544, 699] [45, 151, 220, 289, 440, 474, 545, 700] [46, 152, 221, 290, 441, 475, 546, 701] [47, 153, 222, 291, 442, 476, 547, 702] [48, 154, 223, 292, 443, 477, 548, 703] [49, 155, 224, 293, 444, 478, 549, 704] [50, 156, 225, 294, 356, 479, 550, 705] [51, 157, 226, 295, 357, 480, 551, 706] [52, 158, 227, 296, 358, 481, 552, 707] [53, 159, 228, 297, 359, 482, 553, 708] [54, 160, 229, 298, 360, 483, 554, 709] [55, 161, 230, 299, 361, 484, 555, 710] [56, 162, 231, 300, 362, 485, 556, 711] [57, 163, 232, 301, 363, 486, 557, 623] [58, 164, 233, 302, 364, 487, 558, 624] [59, 165, 234, 303, 365, 488, 559, 625] [60, 166, 235, 304, 366, 489, 560, 626] [61, 167, 236, 305, 367, 490, 561, 627] [62, 168, 237, 306, 368, 491, 562, 628] [63, 169, 238, 307, 369, 492, 563, 629] [64, 170, 239, 308, 370, 493, 564, 630] [65, 171, 240, 309, 371, 494, 565, 631] [66, 172, 241, 310, 372, 495, 566, 632] [67, 173, 242, 311, 373, 496, 567, 633] [68, 174, 243, 312, 374, 497, 568, 634] [69, 175, 244, 313, 375, 498, 569, 635] [70, 176, 245, 314, 376, 499, 570, 636] [71, 177, 246, 315, 377, 500, 571, 637] [72, 89, 247, 316, 378, 501, 572, 638] [73, 90, 248, 317, 379, 502, 573, 639] [74, 91, 249, 318, 380, 503, 574, 640] [75, 92, 250, 319, 381, 504, 575, 641] [76, 93, 251, 320, 382, 505, 576, 642] [77, 94, 252, 321, 383, 506, 577, 643] [78, 95, 253, 322, 384, 507, 578, 644] [79, 96, 254, 323, 385, 508, 579, 645] [80, 97, 255, 324, 386, 509, 580, 646] [81, 98, 256, 325, 387, 510, 581, 647] [82, 99, 257, 326, 388, 511, 582, 648] [83, 100, 258, 327, 389, 512, 583, 649] [84, 101, 259, 328, 390, 513, 584, 650] [85, 102, 260, 329, 391, 514, 585, 651] [86, 103, 261, 330, 392, 515, 586, 652] [87, 104, 262, 331, 393, 516, 587, 653] [88, 105, 263, 332, 394, 517, 588, 654] [0, 106, 264, 333, 395, 518, 589, 655] [1, 107, 265, 334, 396, 519, 590, 656] [2, 108, 266, 335, 397, 520, 591, 657] [3, 109, 178, 336, 398, 521, 592, 658] [4, 110, 179, 337, 399, 522, 593, 659] [5, 111, 180, 338, 400, 523, 594, 660] [6, 112, 181, 339, 401, 524, 595, 661] [7, 113, 182, 340, 402, 525, 596, 662] [8, 114, 183, 341, 403, 526, 597, 663] [9, 115, 184, 342, 404, 527, 598, 664] [10, 116, 185, 343, 405, 528, 599, 665] [11, 117, 186, 344, 406, 529, 600, 666] [12, 118, 187, 345, 407, 530, 601, 667] [13, 119, 188, 346, 408, 531, 602, 668] [14, 120, 189, 347, 409, 532, 603, 669] [41, 89, 197, 342, 435, 516, 610, 649] [42, 90, 198, 343, 436, 517, 611, 650] [43, 91, 199, 344, 437, 518, 612, 651] [44, 92, 200, 345, 438, 519, 613, 652] [45, 93, 201, 346, 439, 520, 614, 653] [46, 94, 202, 347, 440, 521, 615, 654] [47, 95, 203, 348, 441, 522, 616, 655] [48, 96, 204, 349, 442, 523, 617, 656] [49, 97, 205, 350, 443, 524, 618, 657] [50, 98, 206, 351, 444, 525, 619, 658] [51, 99, 207, 352, 356, 526, 620, 659] [52, 100, 208, 353, 357, 527, 621, 660] [53, 101, 209, 354, 358, 528, 622, 661] [54, 102, 210, 355, 359, 529, 534, 662] [55, 103, 211, 267, 360, 530, 535, 663] [56, 104, 212, 268, 361, 531, 536, 664] [57, 105, 213, 269, 362, 532, 537, 665] [58, 106, 214, 270, 363, 533, 538, 666] [59, 107, 215, 271, 364, 445, 539, 667] [60, 108, 216, 272, 365, 446, 540, 668] [61, 109, 217, 273, 366, 447, 541, 669] [62, 110, 218, 274, 367, 448, 542, 670] [63, 111, 219, 275, 368, 449, 543, 671] [64, 112, 220, 276, 369, 450, 544, 672] [65, 113, 221, 277, 370, 451, 545, 673] [66, 114, 222, 278, 371, 452, 546, 674] [67, 115, 223, 279, 372, 453, 547, 675] [68, 116, 224, 280, 373, 454, 548, 676] [69, 117, 225, 281, 374, 455, 549, 677] [70, 118, 226, 282, 375, 456, 550, 678] [71, 119, 227, 283, 376, 457, 551, 679] [72, 120, 228, 284, 377, 458, 552, 680] [73, 121, 229, 285, 378, 459, 553, 681] [74, 122, 230, 286, 379, 460, 554, 682] [75, 123, 231, 287, 380, 461, 555, 683] [76, 124, 232, 288, 381, 462, 556, 684] [77, 125, 233, 289, 382, 463, 557, 685] [78, 126, 234, 290, 383, 464, 558, 686] [79, 127, 235, 291, 384, 465, 559, 687] [80, 128, 236, 292, 385, 466, 560, 688] [81, 129, 237, 293, 386, 467, 561, 689] [82, 130, 238, 294, 387, 468, 562, 690] [83, 131, 239, 295, 388, 469, 563, 691] [84, 132, 240, 296, 389, 470, 564, 692] [85, 133, 241, 297, 390, 471, 565, 693] [86, 134, 242, 298, 391, 472, 566, 694] [87, 135, 243, 299, 392, 473, 567, 695] [88, 136, 244, 300, 393, 474, 568, 696] [0, 137, 245, 301, 394, 475, 569, 697] [1, 138, 246, 302, 395, 476, 570, 698] [2, 139, 247, 303, 396, 477, 571, 699] [3, 140, 248, 304, 397, 478, 572, 700] [4, 141, 249, 305, 398, 479, 573, 701] [5, 142, 250, 306, 399, 480, 574, 702] [6, 143, 251, 307, 400, 481, 575, 703] [7, 144, 252, 308, 401, 482, 576, 704] [8, 145, 253, 309, 402, 483, 577, 705] [9, 146, 254, 310, 403, 484, 578, 706] [10, 147, 255, 311, 404, 485, 579, 707] [11, 148, 256, 312, 405, 486, 580, 708] [12, 149, 257, 313, 406, 487, 581, 709] [13, 150, 258, 314, 407, 488, 582, 710] [14, 151, 259, 315, 408, 489, 583, 711] [15, 152, 260, 316, 409, 490, 584, 623] [16, 153, 261, 317, 410, 491, 585, 624] [17, 154, 262, 318, 411, 492, 586, 625] [18, 155, 263, 319, 412, 493, 587, 626] [19, 156, 264, 320, 413, 494, 588, 627] [20, 157, 265, 321, 414, 495, 589, 628] [21, 158, 266, 322, 415, 496, 590, 629] [22, 159, 178, 323, 416, 497, 591, 630] [23, 160, 179, 324, 417, 498, 592, 631] [24, 161, 180, 325, 418, 499, 593, 632] [25, 162, 181, 326, 419, 500, 594, 633] [26, 163, 182, 327, 420, 501, 595, 634] [27, 164, 183, 328, 421, 502, 596, 635] [28, 165, 184, 329, 422, 503, 597, 636] [29, 166, 185, 330, 423, 504, 598, 637] [30, 167, 186, 331, 424, 505, 599, 638] [31, 168, 187, 332, 425, 506, 600, 639] [32, 169, 188, 333, 426, 507, 601, 640] [33, 170, 189, 334, 427, 508, 602, 641] [34, 171, 190, 335, 428, 509, 603, 642] [35, 172, 191, 336, 429, 510, 604, 643] [36, 173, 192, 337, 430, 511, 605, 644] [37, 174, 193, 338, 431, 512, 606, 645] [38, 175, 194, 339, 432, 513, 607, 646] [39, 176, 195, 340, 433, 514, 608, 647] [40, 177, 196, 341, 434, 515, 609, 648] [25, 136, 192, 309, 435, 475, 621, 704] [26, 137, 193, 310, 436, 476, 622, 705] [27, 138, 194, 311, 437, 477, 534, 706] [28, 139, 195, 312, 438, 478, 535, 707] [29, 140, 196, 313, 439, 479, 536, 708] [30, 141, 197, 314, 440, 480, 537, 709] [31, 142, 198, 315, 441, 481, 538, 710] [32, 143, 199, 316, 442, 482, 539, 711] [33, 144, 200, 317, 443, 483, 540, 623] [34, 145, 201, 318, 444, 484, 541, 624] [35, 146, 202, 319, 356, 485, 542, 625] [36, 147, 203, 320, 357, 486, 543, 626] [37, 148, 204, 321, 358, 487, 544, 627] [38, 149, 205, 322, 359, 488, 545, 628] [39, 150, 206, 323, 360, 489, 546, 629] [40, 151, 207, 324, 361, 490, 547, 630] [41, 152, 208, 325, 362, 491, 548, 631] [42, 153, 209, 326, 363, 492, 549, 632] [43, 154, 210, 327, 364, 493, 550, 633] [44, 155, 211, 328, 365, 494, 551, 634] [45, 156, 212, 329, 366, 495, 552, 635] [46, 157, 213, 330, 367, 496, 553, 636] [47, 158, 214, 331, 368, 497, 554, 637] [48, 159, 215, 332, 369, 498, 555, 638] [49, 160, 216, 333, 370, 499, 556, 639] [50, 161, 217, 334, 371, 500, 557, 640] [51, 162, 218, 335, 372, 501, 558, 641] [52, 163, 219, 336, 373, 502, 559, 642] [53, 164, 220, 337, 374, 503, 560, 643] [54, 165, 221, 338, 375, 504, 561, 644] [55, 166, 222, 339, 376, 505, 562, 645] [56, 167, 223, 340, 377, 506, 563, 646] [57, 168, 224, 341, 378, 507, 564, 647] [58, 169, 225, 342, 379, 508, 565, 648] [59, 170, 226, 343, 380, 509, 566, 649] [60, 171, 227, 344, 381, 510, 567, 650] [61, 172, 228, 345, 382, 511, 568, 651] [62, 173, 229, 346, 383, 512, 569, 652] [63, 174, 230, 347, 384, 513, 570, 653] [64, 175, 231, 348, 385, 514, 571, 654] [65, 176, 232, 349, 386, 515, 572, 655] [66, 177, 233, 350, 387, 516, 573, 656] [67, 89, 234, 351, 388, 517, 574, 657] [68, 90, 235, 352, 389, 518, 575, 658] [69, 91, 236, 353, 390, 519, 576, 659] [70, 92, 237, 354, 391, 520, 577, 660] [71, 93, 238, 355, 392, 521, 578, 661] [72, 94, 239, 267, 393, 522, 579, 662] [73, 95, 240, 268, 394, 523, 580, 663] [74, 96, 241, 269, 395, 524, 581, 664] [75, 97, 242, 270, 396, 525, 582, 665] [76, 98, 243, 271, 397, 526, 583, 666] [77, 99, 244, 272, 398, 527, 584, 667] [78, 100, 245, 273, 399, 528, 585, 668] [79, 101, 246, 274, 400, 529, 586, 669] [80, 102, 247, 275, 401, 530, 587, 670] [81, 103, 248, 276, 402, 531, 588, 671] [82, 104, 249, 277, 403, 532, 589, 672] [83, 105, 250, 278, 404, 533, 590, 673] [84, 106, 251, 279, 405, 445, 591, 674] [85, 107, 252, 280, 406, 446, 592, 675] [86, 108, 253, 281, 407, 447, 593, 676] [87, 109, 254, 282, 408, 448, 594, 677] [88, 110, 255, 283, 409, 449, 595, 678] [0, 111, 256, 284, 410, 450, 596, 679] [1, 112, 257, 285, 411, 451, 597, 680] [2, 113, 258, 286, 412, 452, 598, 681] [3, 114, 259, 287, 413, 453, 599, 682] [4, 115, 260, 288, 414, 454, 600, 683] [5, 116, 261, 289, 415, 455, 601, 684] [6, 117, 262, 290, 416, 456, 602, 685] [7, 118, 263, 291, 417, 457, 603, 686] [8, 119, 264, 292, 418, 458, 604, 687] [9, 120, 265, 293, 419, 459, 605, 688] [10, 121, 266, 294, 420, 460, 606, 689] [11, 122, 178, 295, 421, 461, 607, 690] [12, 123, 179, 296, 422, 462, 608, 691] [13, 124, 180, 297, 423, 463, 609, 692] [14, 125, 181, 298, 424, 464, 610, 693] [15, 126, 182, 299, 425, 465, 611, 694] [16, 127, 183, 300, 426, 466, 612, 695] [17, 128, 184, 301, 427, 467, 613, 696] [18, 129, 185, 302, 428, 468, 614, 697] [19, 130, 186, 303, 429, 469, 615, 698] [20, 131, 187, 304, 430, 470, 616, 699] [21, 132, 188, 305, 431, 471, 617, 700] [22, 133, 189, 306, 432, 472, 618, 701] [23, 134, 190, 307, 433, 473, 619, 702] [24, 135, 191, 308, 434, 474, 620, 703]
H_Z (267 checks, sparse supports)
[22, 170, 189, 324, 417, 509, 603, 630] [23, 171, 190, 325, 418, 510, 604, 631] [24, 172, 191, 326, 419, 511, 605, 632] [25, 173, 192, 327, 420, 512, 606, 633] [26, 174, 193, 328, 421, 513, 607, 634] [27, 175, 194, 329, 422, 514, 608, 635] [28, 176, 195, 330, 423, 515, 609, 636] [29, 177, 196, 331, 424, 516, 610, 637] [30, 89, 197, 332, 425, 517, 611, 638] [31, 90, 198, 333, 426, 518, 612, 639] [32, 91, 199, 334, 427, 519, 613, 640] [33, 92, 200, 335, 428, 520, 614, 641] [34, 93, 201, 336, 429, 521, 615, 642] [35, 94, 202, 337, 430, 522, 616, 643] [36, 95, 203, 338, 431, 523, 617, 644] [37, 96, 204, 339, 432, 524, 618, 645] [38, 97, 205, 340, 433, 525, 619, 646] [39, 98, 206, 341, 434, 526, 620, 647] [40, 99, 207, 342, 435, 527, 621, 648] [41, 100, 208, 343, 436, 528, 622, 649] [42, 101, 209, 344, 437, 529, 534, 650] [43, 102, 210, 345, 438, 530, 535, 651] [44, 103, 211, 346, 439, 531, 536, 652] [45, 104, 212, 347, 440, 532, 537, 653] [46, 105, 213, 348, 441, 533, 538, 654] [47, 106, 214, 349, 442, 445, 539, 655] [48, 107, 215, 350, 443, 446, 540, 656] [49, 108, 216, 351, 444, 447, 541, 657] [50, 109, 217, 352, 356, 448, 542, 658] [51, 110, 218, 353, 357, 449, 543, 659] [52, 111, 219, 354, 358, 450, 544, 660] [53, 112, 220, 355, 359, 451, 545, 661] [54, 113, 221, 267, 360, 452, 546, 662] [55, 114, 222, 268, 361, 453, 547, 663] [56, 115, 223, 269, 362, 454, 548, 664] [57, 116, 224, 270, 363, 455, 549, 665] [58, 117, 225, 271, 364, 456, 550, 666] [59, 118, 226, 272, 365, 457, 551, 667] [60, 119, 227, 273, 366, 458, 552, 668] [61, 120, 228, 274, 367, 459, 553, 669] [62, 121, 229, 275, 368, 460, 554, 670] [63, 122, 230, 276, 369, 461, 555, 671] [64, 123, 231, 277, 370, 462, 556, 672] [65, 124, 232, 278, 371, 463, 557, 673] [66, 125, 233, 279, 372, 464, 558, 674] [67, 126, 234, 280, 373, 465, 559, 675] [68, 127, 235, 281, 374, 466, 560, 676] [69, 128, 236, 282, 375, 467, 561, 677] [70, 129, 237, 283, 376, 468, 562, 678] [71, 130, 238, 284, 377, 469, 563, 679] [72, 131, 239, 285, 378, 470, 564, 680] [73, 132, 240, 286, 379, 471, 565, 681] [74, 133, 241, 287, 380, 472, 566, 682] [75, 134, 242, 288, 381, 473, 567, 683] [76, 135, 243, 289, 382, 474, 568, 684] [77, 136, 244, 290, 383, 475, 569, 685] [78, 137, 245, 291, 384, 476, 570, 686] [79, 138, 246, 292, 385, 477, 571, 687] [80, 139, 247, 293, 386, 478, 572, 688] [81, 140, 248, 294, 387, 479, 573, 689] [82, 141, 249, 295, 388, 480, 574, 690] [83, 142, 250, 296, 389, 481, 575, 691] [84, 143, 251, 297, 390, 482, 576, 692] [85, 144, 252, 298, 391, 483, 577, 693] [86, 145, 253, 299, 392, 484, 578, 694] [87, 146, 254, 300, 393, 485, 579, 695] [88, 147, 255, 301, 394, 486, 580, 696] [0, 148, 256, 302, 395, 487, 581, 697] [1, 149, 257, 303, 396, 488, 582, 698] [2, 150, 258, 304, 397, 489, 583, 699] [3, 151, 259, 305, 398, 490, 584, 700] [4, 152, 260, 306, 399, 491, 585, 701] [5, 153, 261, 307, 400, 492, 586, 702] [6, 154, 262, 308, 401, 493, 587, 703] [7, 155, 263, 309, 402, 494, 588, 704] [8, 156, 264, 310, 403, 495, 589, 705] [9, 157, 265, 311, 404, 496, 590, 706] [10, 158, 266, 312, 405, 497, 591, 707] [11, 159, 178, 313, 406, 498, 592, 708] [12, 160, 179, 314, 407, 499, 593, 709] [13, 161, 180, 315, 408, 500, 594, 710] [14, 162, 181, 316, 409, 501, 595, 711] [15, 163, 182, 317, 410, 502, 596, 623] [16, 164, 183, 318, 411, 503, 597, 624] [17, 165, 184, 319, 412, 504, 598, 625] [18, 166, 185, 320, 413, 505, 599, 626] [19, 167, 186, 321, 414, 506, 600, 627] [20, 168, 187, 322, 415, 507, 601, 628] [21, 169, 188, 323, 416, 508, 602, 629] [0, 119, 264, 268, 394, 531, 588, 679] [1, 120, 265, 269, 395, 532, 589, 680] [2, 121, 266, 270, 396, 533, 590, 681] [3, 122, 178, 271, 397, 445, 591, 682] [4, 123, 179, 272, 398, 446, 592, 683] [5, 124, 180, 273, 399, 447, 593, 684] [6, 125, 181, 274, 400, 448, 594, 685] [7, 126, 182, 275, 401, 449, 595, 686] [8, 127, 183, 276, 402, 450, 596, 687] [9, 128, 184, 277, 403, 451, 597, 688] [10, 129, 185, 278, 404, 452, 598, 689] [11, 130, 186, 279, 405, 453, 599, 690] [12, 131, 187, 280, 406, 454, 600, 691] [13, 132, 188, 281, 407, 455, 601, 692] [14, 133, 189, 282, 408, 456, 602, 693] [15, 134, 190, 283, 409, 457, 603, 694] [16, 135, 191, 284, 410, 458, 604, 695] [17, 136, 192, 285, 411, 459, 605, 696] [18, 137, 193, 286, 412, 460, 606, 697] [19, 138, 194, 287, 413, 461, 607, 698] [20, 139, 195, 288, 414, 462, 608, 699] [21, 140, 196, 289, 415, 463, 609, 700] [22, 141, 197, 290, 416, 464, 610, 701] [23, 142, 198, 291, 417, 465, 611, 702] [24, 143, 199, 292, 418, 466, 612, 703] [25, 144, 200, 293, 419, 467, 613, 704] [26, 145, 201, 294, 420, 468, 614, 705] [27, 146, 202, 295, 421, 469, 615, 706] [28, 147, 203, 296, 422, 470, 616, 707] [29, 148, 204, 297, 423, 471, 617, 708] [30, 149, 205, 298, 424, 472, 618, 709] [31, 150, 206, 299, 425, 473, 619, 710] [32, 151, 207, 300, 426, 474, 620, 711] [33, 152, 208, 301, 427, 475, 621, 623] [34, 153, 209, 302, 428, 476, 622, 624] [35, 154, 210, 303, 429, 477, 534, 625] [36, 155, 211, 304, 430, 478, 535, 626] [37, 156, 212, 305, 431, 479, 536, 627] [38, 157, 213, 306, 432, 480, 537, 628] [39, 158, 214, 307, 433, 481, 538, 629] [40, 159, 215, 308, 434, 482, 539, 630] [41, 160, 216, 309, 435, 483, 540, 631] [42, 161, 217, 310, 436, 484, 541, 632] [43, 162, 218, 311, 437, 485, 542, 633] [44, 163, 219, 312, 438, 486, 543, 634] [45, 164, 220, 313, 439, 487, 544, 635] [46, 165, 221, 314, 440, 488, 545, 636] [47, 166, 222, 315, 441, 489, 546, 637] [48, 167, 223, 316, 442, 490, 547, 638] [49, 168, 224, 317, 443, 491, 548, 639] [50, 169, 225, 318, 444, 492, 549, 640] [51, 170, 226, 319, 356, 493, 550, 641] [52, 171, 227, 320, 357, 494, 551, 642] [53, 172, 228, 321, 358, 495, 552, 643] [54, 173, 229, 322, 359, 496, 553, 644] [55, 174, 230, 323, 360, 497, 554, 645] [56, 175, 231, 324, 361, 498, 555, 646] [57, 176, 232, 325, 362, 499, 556, 647] [58, 177, 233, 326, 363, 500, 557, 648] [59, 89, 234, 327, 364, 501, 558, 649] [60, 90, 235, 328, 365, 502, 559, 650] [61, 91, 236, 329, 366, 503, 560, 651] [62, 92, 237, 330, 367, 504, 561, 652] [63, 93, 238, 331, 368, 505, 562, 653] [64, 94, 239, 332, 369, 506, 563, 654] [65, 95, 240, 333, 370, 507, 564, 655] [66, 96, 241, 334, 371, 508, 565, 656] [67, 97, 242, 335, 372, 509, 566, 657] [68, 98, 243, 336, 373, 510, 567, 658] [69, 99, 244, 337, 374, 511, 568, 659] [70, 100, 245, 338, 375, 512, 569, 660] [71, 101, 246, 339, 376, 513, 570, 661] [72, 102, 247, 340, 377, 514, 571, 662] [73, 103, 248, 341, 378, 515, 572, 663] [74, 104, 249, 342, 379, 516, 573, 664] [75, 105, 250, 343, 380, 517, 574, 665] [76, 106, 251, 344, 381, 518, 575, 666] [77, 107, 252, 345, 382, 519, 576, 667] [78, 108, 253, 346, 383, 520, 577, 668] [79, 109, 254, 347, 384, 521, 578, 669] [80, 110, 255, 348, 385, 522, 579, 670] [81, 111, 256, 349, 386, 523, 580, 671] [82, 112, 257, 350, 387, 524, 581, 672] [83, 113, 258, 351, 388, 525, 582, 673] [84, 114, 259, 352, 389, 526, 583, 674] [85, 115, 260, 353, 390, 527, 584, 675] [86, 116, 261, 354, 391, 528, 585, 676] [87, 117, 262, 355, 392, 529, 586, 677] [88, 118, 263, 267, 393, 530, 587, 678] [2, 89, 247, 350, 412, 516, 587, 657] [3, 90, 248, 351, 413, 517, 588, 658] [4, 91, 249, 352, 414, 518, 589, 659] [5, 92, 250, 353, 415, 519, 590, 660] [6, 93, 251, 354, 416, 520, 591, 661] [7, 94, 252, 355, 417, 521, 592, 662] [8, 95, 253, 267, 418, 522, 593, 663] [9, 96, 254, 268, 419, 523, 594, 664] [10, 97, 255, 269, 420, 524, 595, 665] [11, 98, 256, 270, 421, 525, 596, 666] [12, 99, 257, 271, 422, 526, 597, 667] [13, 100, 258, 272, 423, 527, 598, 668] [14, 101, 259, 273, 424, 528, 599, 669] [15, 102, 260, 274, 425, 529, 600, 670] [16, 103, 261, 275, 426, 530, 601, 671] [17, 104, 262, 276, 427, 531, 602, 672] [18, 105, 263, 277, 428, 532, 603, 673] [19, 106, 264, 278, 429, 533, 604, 674] [20, 107, 265, 279, 430, 445, 605, 675] [21, 108, 266, 280, 431, 446, 606, 676] [22, 109, 178, 281, 432, 447, 607, 677] [23, 110, 179, 282, 433, 448, 608, 678] [24, 111, 180, 283, 434, 449, 609, 679] [25, 112, 181, 284, 435, 450, 610, 680] [26, 113, 182, 285, 436, 451, 611, 681] [27, 114, 183, 286, 437, 452, 612, 682] [28, 115, 184, 287, 438, 453, 613, 683] [29, 116, 185, 288, 439, 454, 614, 684] [30, 117, 186, 289, 440, 455, 615, 685] [31, 118, 187, 290, 441, 456, 616, 686] [32, 119, 188, 291, 442, 457, 617, 687] [33, 120, 189, 292, 443, 458, 618, 688] [34, 121, 190, 293, 444, 459, 619, 689] [35, 122, 191, 294, 356, 460, 620, 690] [36, 123, 192, 295, 357, 461, 621, 691] [37, 124, 193, 296, 358, 462, 622, 692] [38, 125, 194, 297, 359, 463, 534, 693] [39, 126, 195, 298, 360, 464, 535, 694] [40, 127, 196, 299, 361, 465, 536, 695] [41, 128, 197, 300, 362, 466, 537, 696] [42, 129, 198, 301, 363, 467, 538, 697] [43, 130, 199, 302, 364, 468, 539, 698] [44, 131, 200, 303, 365, 469, 540, 699] [45, 132, 201, 304, 366, 470, 541, 700] [46, 133, 202, 305, 367, 471, 542, 701] [47, 134, 203, 306, 368, 472, 543, 702] [48, 135, 204, 307, 369, 473, 544, 703] [49, 136, 205, 308, 370, 474, 545, 704] [50, 137, 206, 309, 371, 475, 546, 705] [51, 138, 207, 310, 372, 476, 547, 706] [52, 139, 208, 311, 373, 477, 548, 707] [53, 140, 209, 312, 374, 478, 549, 708] [54, 141, 210, 313, 375, 479, 550, 709] [55, 142, 211, 314, 376, 480, 551, 710] [56, 143, 212, 315, 377, 481, 552, 711] [57, 144, 213, 316, 378, 482, 553, 623] [58, 145, 214, 317, 379, 483, 554, 624] [59, 146, 215, 318, 380, 484, 555, 625] [60, 147, 216, 319, 381, 485, 556, 626] [61, 148, 217, 320, 382, 486, 557, 627] [62, 149, 218, 321, 383, 487, 558, 628] [63, 150, 219, 322, 384, 488, 559, 629] [64, 151, 220, 323, 385, 489, 560, 630] [65, 152, 221, 324, 386, 490, 561, 631] [66, 153, 222, 325, 387, 491, 562, 632] [67, 154, 223, 326, 388, 492, 563, 633] [68, 155, 224, 327, 389, 493, 564, 634] [69, 156, 225, 328, 390, 494, 565, 635] [70, 157, 226, 329, 391, 495, 566, 636] [71, 158, 227, 330, 392, 496, 567, 637] [72, 159, 228, 331, 393, 497, 568, 638] [73, 160, 229, 332, 394, 498, 569, 639] [74, 161, 230, 333, 395, 499, 570, 640] [75, 162, 231, 334, 396, 500, 571, 641] [76, 163, 232, 335, 397, 501, 572, 642] [77, 164, 233, 336, 398, 502, 573, 643] [78, 165, 234, 337, 399, 503, 574, 644] [79, 166, 235, 338, 400, 504, 575, 645] [80, 167, 236, 339, 401, 505, 576, 646] [81, 168, 237, 340, 402, 506, 577, 647] [82, 169, 238, 341, 403, 507, 578, 648] [83, 170, 239, 342, 404, 508, 579, 649] [84, 171, 240, 343, 405, 509, 580, 650] [85, 172, 241, 344, 406, 510, 581, 651] [86, 173, 242, 345, 407, 511, 582, 652] [87, 174, 243, 346, 408, 512, 583, 653] [88, 175, 244, 347, 409, 513, 584, 654] [0, 176, 245, 348, 410, 514, 585, 655] [1, 177, 246, 349, 411, 515, 586, 656]
Code ID 712-182-20 · download JSON · raw on GitHub