← back to the board
[[776,198,20]] d ≤
n
776
k
198
d
20
kd²/n
102.062
w
8
X/Z
1

Share this result

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 106 trials · survived 5.9×107 trials · 2026-09-23
witness operator (support, 20 qubits)
[51, 70, 128, 147, 184, 196, 264, 309, 315, 368, 440, 478, 506, 544, 578, 643, 650, 696, 740, 774]
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 106 trials · survived 5.9×107 trials · 2026-09-23
witness operator (support, 20 qubits)
[106, 119, 141, 205, 283, 290, 300, 384, 394, 430, 500, 519, 566, 569, 657, 659, 669, 699, 737, 753]
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)×776 (2,4)×8148 (3,5)×114072 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 776 (2,4): 8148 (3,5): 114072 (3,7): 16296
trapping sets H_Z (1,3)×776 (2,4)×8148 (3,5)×114072 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 776 (2,4): 8148 (3,5): 114072 (3,7): 16296

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=97, n=8P=776, k=2P+4=198. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_97: E_x = [[29, 20, 44, 46, 25, 49, 53, 9], [91, 93, 62, 65, 12, 87, 93, 63], [88, 45, 40, 58, 49, 17, 14, 78]], E_z = [[68, 51, 20, 20, 64, 23, 29, 40], [71, 91, 86, 1, 89, 23, 20, 61], [46, 90, 17, 28, 7, 84, 88, 26]]. 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). Same construction and design system as the board's [[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 2026-09-23
notes Found by a GPU random-information-set screen (deep kernel: full-basis RREF plus pair sums) over pair-partition CPM (3,8) codes at prime lifts P in {89, 97, 101, 103, 107, 109, 113} at n in [702, 1000]; see the research note for the ladder. Lightest logicals: X 20, Z 20; deep-kernel GPU passes (full basis, pair depth 8): X 20 at 50,000,000 trials (seed 777); Z 20 at 50,000,000 trials (seed 778); board fast pass 20 at 8,000,000 trials. Every operator re-verified with verify/gf2.py. Distance is a witness-backed upper bound. 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": 97, "E": [[29, 20, 44, 46, 25, 49, 53, 9], [91, 93, 62, 65, 12, 87, 93, 63], [88, 45, 40, 58, 49, 17, 14, 78]], "D": [[68, 51, 20, 20, 64, 23, 29, 40], [71, 91, 86, 1, 89, 23, 20, 61], [46, 90, 17, 28, 7, 84, 88, 26]]}
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

[[776,198,20]] pair-partition CPM (3,8) code at prime lift P = 97

Direction & hypothesis

Cell: unrestricted x weight-8, extended tier (n in (700, 1000], w <= 8, d <= 40). The cell's high-rate end is held by the pair-partition CPM family of arXiv:2607.14091 at P = 73, 79, 83 (d = 18) and P = 101 ([[808,206,20]], kd^2/n = 101.98). In this family n = 8P and k = 2P + 4, so the score is d^2 (1/4 + 1/(2P)): a d = 20 member at a lift below 101 scores above the P = 101 entry, and P = 89 and P = 97 are the two admissible lifts (n = 712, 776) with no board entry. The hypothesis was that d = 20 draws exist at those lifts, since the P = 101 entry already reaches 20 and the family's distance rises with P.

What was searched

  • Random solutions of the (3,8) pair-partition design system over F_P for

    • P in {89, 97, 101, 103, 107, 109, 113}: 36 equations in 48 unknowns, nullity 19; a random null-space vector gives the exponent arrays E_x, E_z; draws with a 4- or 6-cycle in either array are discarded (girth 8, as in the paper). The builder was checked to rebuild codes/808-206-20.json bit for bit from its published arrays.

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

    • pair depth 8), in three stages per side, 50,000, 300,000, and 1,000,000 trials, with early stop as soon as a logical lighter than the threshold appears (20 at P = 89, 97; 21 at P >= 101). The 64-row sketch kernel was tried first on this family and abandoned: its 20,000,000-trial bounds of 22 to 24 on P = 109 and 113 draws all fell to 18 to 20 under a full-basis search, so only the deep kernel was used for the run that produced this code.

  • 2700 girth-8 draws in that run (seed 61, batches of 12), 288,400,000

    • GPU trials, 5.93 GPU hours on one NVIDIA A40:

| P | n | draws | lightest logical found per draw (deep-kernel screen, up to 1,000,000 trials per side) | |---:|---:|---:|---| | 89 | 712 | 258 | 6: 1, 8: 7, 10: 2, 12: 41, 14: 45, 16: 132, 18: 30 | | 97 | 776 | 310 | 8: 7, 10: 2, 12: 42, 14: 49, 16: 140, 18: 67, 20: 3 | | 101 | 808 | 379 | 8: 6, 10: 4, 12: 45, 14: 41, 16: 167, 18: 98, 20: 18 | | 103 | 824 | 392 | 8: 7, 10: 4, 12: 50, 14: 39, 16: 167, 18: 110, 20: 15 | | 107 | 856 | 421 | 8: 4, 10: 1, 12: 49, 14: 31, 16: 173, 18: 123, 20: 40 | | 109 | 872 | 499 | 8: 10, 10: 5, 12: 51, 14: 36, 16: 209, 18: 136, 20: 52 | | 113 | 904 | 441 | 8: 5, 10: 1, 12: 37, 14: 32, 16: 174, 18: 139, 20: 53 |

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 | 50,000 | 61000005021 | 20 | | screen stage 1, GPU deep kernel (full basis, pair depth 8) | Z | 50,000 | 61000005022 | 20 | | screen stage 2, GPU deep kernel (full basis, pair depth 8) | X | 300,000 | 61000005300 | 20 | | screen stage 2, GPU deep kernel (full basis, pair depth 8) | Z | 300,000 | 61000005301 | 20 | | screen stage 3, GPU deep kernel (full basis, pair depth 8) (recover) | X | 1,000,000 | 61000005600 | 20 | | screen stage 3, GPU deep kernel (full basis, pair depth 8) (recover) | Z | 1,000,000 | 61000005601 | 20 | | finalist GPU deep kernel (full basis, pair depth 8) | X | 50,000,000 | 777 | 20 | | finalist GPU deep kernel (full basis, pair depth 8) | Z | 50,000,000 | 778 | 20 | | board fast pass, gf2_fast pair depth 8, 3 threads, both sides | both | 8,000,000 | 2209 | 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):

  • full pass (8,000,000-trial fast pass, uncapped, 3 threads): validate_candidate passed = True (its 8000-trial pure-Python refute_check found nothing lighter); gf2_fast fast pass: lightest logical 20 at 8,000,000 trials (14003 s).

Claim: witness-backed upper bound d <= 20 (X <= 20, Z <= 20), not exact. Both sides read 20 at every rung from 50,000 to 50,000,000 deep-kernel trials. The family's distance is bounded above by (J+1)! = 24, so 20 is within two steps of the ceiling.

Dead ends

  • Sketch-kernel screening of this family: 288 draws at P in {89, ..., 113},

    • 48 read 20 to 24 at 20,000,000 sketch trials per side, every one that was checked with a full-basis search came out at 18 to 20; a P = 97 draw that read 20 (X) and 22 (Z) after a 50,000,000-trial sketch pass fell to 18 on both sides after 5,000,000 deep-kernel trials.

  • No draw at any P reached 21 in this run or in the 108-draw deep-kernel run

    • that preceded it; d = 20 at P = 103, 109, 113 recurs but does not beat the P = 101 entry.

  • P = 89 (n = 712): 258 draws, none above 18.

Tools

Model: Claude Fable 5.1 (Claude Code), matching provenance.model. 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 and girth filter are a few dozen lines of Python (Gaussian elimination over F_P, cycle enumeration over the 3 x 8 arrays), described in full above.

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=97, n=8P=776, k=2P+4=198. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_97: E_x = [[29, 20, 44, 46, 25, 49, 53, 9], [91, 93, 62, 65, 12, 87, 93, 63], [88, 45, 40, 58, 49, 17, 14, 78]], E_z = [[68, 51, 20, 20, 64, 23, 29, 40], [71, 91, 86, 1, 89, 23, 20, 61], [46, 90, 17, 28, 7, 84, 88, 26]]. 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). Same construction and design system as the board's [[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 291 (max weight 8) · Z-checks 291 (max weight 8)
H_X (291 checks, sparse supports)
[68, 174, 247, 342, 460, 533, 626, 767] [69, 175, 248, 343, 461, 534, 627, 768] [70, 176, 249, 344, 462, 535, 628, 769] [71, 177, 250, 345, 463, 536, 629, 770] [72, 178, 251, 346, 464, 537, 630, 771] [73, 179, 252, 347, 465, 538, 631, 772] [74, 180, 253, 348, 466, 539, 632, 773] [75, 181, 254, 349, 467, 540, 633, 774] [76, 182, 255, 350, 468, 541, 634, 775] [77, 183, 256, 351, 469, 542, 635, 679] [78, 184, 257, 352, 470, 543, 636, 680] [79, 185, 258, 353, 471, 544, 637, 681] [80, 186, 259, 354, 472, 545, 638, 682] [81, 187, 260, 355, 473, 546, 639, 683] [82, 188, 261, 356, 474, 547, 640, 684] [83, 189, 262, 357, 475, 548, 641, 685] [84, 190, 263, 358, 476, 549, 642, 686] [85, 191, 264, 359, 477, 550, 643, 687] [86, 192, 265, 360, 478, 551, 644, 688] [87, 193, 266, 361, 479, 552, 645, 689] [88, 97, 267, 362, 480, 553, 646, 690] [89, 98, 268, 363, 481, 554, 647, 691] [90, 99, 269, 364, 482, 555, 648, 692] [91, 100, 270, 365, 483, 556, 649, 693] [92, 101, 271, 366, 484, 557, 650, 694] [93, 102, 272, 367, 388, 558, 651, 695] [94, 103, 273, 368, 389, 559, 652, 696] [95, 104, 274, 369, 390, 560, 653, 697] [96, 105, 275, 370, 391, 561, 654, 698] [0, 106, 276, 371, 392, 562, 655, 699] [1, 107, 277, 372, 393, 563, 656, 700] [2, 108, 278, 373, 394, 564, 657, 701] [3, 109, 279, 374, 395, 565, 658, 702] [4, 110, 280, 375, 396, 566, 659, 703] [5, 111, 281, 376, 397, 567, 660, 704] [6, 112, 282, 377, 398, 568, 661, 705] [7, 113, 283, 378, 399, 569, 662, 706] [8, 114, 284, 379, 400, 570, 663, 707] [9, 115, 285, 380, 401, 571, 664, 708] [10, 116, 286, 381, 402, 572, 665, 709] [11, 117, 287, 382, 403, 573, 666, 710] [12, 118, 288, 383, 404, 574, 667, 711] [13, 119, 289, 384, 405, 575, 668, 712] [14, 120, 290, 385, 406, 576, 669, 713] [15, 121, 194, 386, 407, 577, 670, 714] [16, 122, 195, 387, 408, 578, 671, 715] [17, 123, 196, 291, 409, 579, 672, 716] [18, 124, 197, 292, 410, 580, 673, 717] [19, 125, 198, 293, 411, 581, 674, 718] [20, 126, 199, 294, 412, 485, 675, 719] [21, 127, 200, 295, 413, 486, 676, 720] [22, 128, 201, 296, 414, 487, 677, 721] [23, 129, 202, 297, 415, 488, 678, 722] [24, 130, 203, 298, 416, 489, 582, 723] [25, 131, 204, 299, 417, 490, 583, 724] [26, 132, 205, 300, 418, 491, 584, 725] [27, 133, 206, 301, 419, 492, 585, 726] [28, 134, 207, 302, 420, 493, 586, 727] [29, 135, 208, 303, 421, 494, 587, 728] [30, 136, 209, 304, 422, 495, 588, 729] [31, 137, 210, 305, 423, 496, 589, 730] [32, 138, 211, 306, 424, 497, 590, 731] [33, 139, 212, 307, 425, 498, 591, 732] [34, 140, 213, 308, 426, 499, 592, 733] [35, 141, 214, 309, 427, 500, 593, 734] [36, 142, 215, 310, 428, 501, 594, 735] [37, 143, 216, 311, 429, 502, 595, 736] [38, 144, 217, 312, 430, 503, 596, 737] [39, 145, 218, 313, 431, 504, 597, 738] [40, 146, 219, 314, 432, 505, 598, 739] [41, 147, 220, 315, 433, 506, 599, 740] [42, 148, 221, 316, 434, 507, 600, 741] [43, 149, 222, 317, 435, 508, 601, 742] [44, 150, 223, 318, 436, 509, 602, 743] [45, 151, 224, 319, 437, 510, 603, 744] [46, 152, 225, 320, 438, 511, 604, 745] [47, 153, 226, 321, 439, 512, 605, 746] [48, 154, 227, 322, 440, 513, 606, 747] [49, 155, 228, 323, 441, 514, 607, 748] [50, 156, 229, 324, 442, 515, 608, 749] [51, 157, 230, 325, 443, 516, 609, 750] [52, 158, 231, 326, 444, 517, 610, 751] [53, 159, 232, 327, 445, 518, 611, 752] [54, 160, 233, 328, 446, 519, 612, 753] [55, 161, 234, 329, 447, 520, 613, 754] [56, 162, 235, 330, 448, 521, 614, 755] [57, 163, 236, 331, 449, 522, 615, 756] [58, 164, 237, 332, 450, 523, 616, 757] [59, 165, 238, 333, 451, 524, 617, 758] [60, 166, 239, 334, 452, 525, 618, 759] [61, 167, 240, 335, 453, 526, 619, 760] [62, 168, 241, 336, 454, 527, 620, 761] [63, 169, 242, 337, 455, 528, 621, 762] [64, 170, 243, 338, 456, 529, 622, 763] [65, 171, 244, 339, 457, 530, 623, 764] [66, 172, 245, 340, 458, 531, 624, 765] [67, 173, 246, 341, 459, 532, 625, 766] [6, 101, 229, 323, 473, 495, 586, 713] [7, 102, 230, 324, 474, 496, 587, 714] [8, 103, 231, 325, 475, 497, 588, 715] [9, 104, 232, 326, 476, 498, 589, 716] [10, 105, 233, 327, 477, 499, 590, 717] [11, 106, 234, 328, 478, 500, 591, 718] [12, 107, 235, 329, 479, 501, 592, 719] [13, 108, 236, 330, 480, 502, 593, 720] [14, 109, 237, 331, 481, 503, 594, 721] [15, 110, 238, 332, 482, 504, 595, 722] [16, 111, 239, 333, 483, 505, 596, 723] [17, 112, 240, 334, 484, 506, 597, 724] [18, 113, 241, 335, 388, 507, 598, 725] [19, 114, 242, 336, 389, 508, 599, 726] [20, 115, 243, 337, 390, 509, 600, 727] [21, 116, 244, 338, 391, 510, 601, 728] [22, 117, 245, 339, 392, 511, 602, 729] [23, 118, 246, 340, 393, 512, 603, 730] [24, 119, 247, 341, 394, 513, 604, 731] [25, 120, 248, 342, 395, 514, 605, 732] [26, 121, 249, 343, 396, 515, 606, 733] [27, 122, 250, 344, 397, 516, 607, 734] [28, 123, 251, 345, 398, 517, 608, 735] [29, 124, 252, 346, 399, 518, 609, 736] [30, 125, 253, 347, 400, 519, 610, 737] [31, 126, 254, 348, 401, 520, 611, 738] [32, 127, 255, 349, 402, 521, 612, 739] [33, 128, 256, 350, 403, 522, 613, 740] [34, 129, 257, 351, 404, 523, 614, 741] [35, 130, 258, 352, 405, 524, 615, 742] [36, 131, 259, 353, 406, 525, 616, 743] [37, 132, 260, 354, 407, 526, 617, 744] [38, 133, 261, 355, 408, 527, 618, 745] [39, 134, 262, 356, 409, 528, 619, 746] [40, 135, 263, 357, 410, 529, 620, 747] [41, 136, 264, 358, 411, 530, 621, 748] [42, 137, 265, 359, 412, 531, 622, 749] [43, 138, 266, 360, 413, 532, 623, 750] [44, 139, 267, 361, 414, 533, 624, 751] [45, 140, 268, 362, 415, 534, 625, 752] [46, 141, 269, 363, 416, 535, 626, 753] [47, 142, 270, 364, 417, 536, 627, 754] [48, 143, 271, 365, 418, 537, 628, 755] [49, 144, 272, 366, 419, 538, 629, 756] [50, 145, 273, 367, 420, 539, 630, 757] [51, 146, 274, 368, 421, 540, 631, 758] [52, 147, 275, 369, 422, 541, 632, 759] [53, 148, 276, 370, 423, 542, 633, 760] [54, 149, 277, 371, 424, 543, 634, 761] [55, 150, 278, 372, 425, 544, 635, 762] [56, 151, 279, 373, 426, 545, 636, 763] [57, 152, 280, 374, 427, 546, 637, 764] [58, 153, 281, 375, 428, 547, 638, 765] [59, 154, 282, 376, 429, 548, 639, 766] [60, 155, 283, 377, 430, 549, 640, 767] [61, 156, 284, 378, 431, 550, 641, 768] [62, 157, 285, 379, 432, 551, 642, 769] [63, 158, 286, 380, 433, 552, 643, 770] [64, 159, 287, 381, 434, 553, 644, 771] [65, 160, 288, 382, 435, 554, 645, 772] [66, 161, 289, 383, 436, 555, 646, 773] [67, 162, 290, 384, 437, 556, 647, 774] [68, 163, 194, 385, 438, 557, 648, 775] [69, 164, 195, 386, 439, 558, 649, 679] [70, 165, 196, 387, 440, 559, 650, 680] [71, 166, 197, 291, 441, 560, 651, 681] [72, 167, 198, 292, 442, 561, 652, 682] [73, 168, 199, 293, 443, 562, 653, 683] [74, 169, 200, 294, 444, 563, 654, 684] [75, 170, 201, 295, 445, 564, 655, 685] [76, 171, 202, 296, 446, 565, 656, 686] [77, 172, 203, 297, 447, 566, 657, 687] [78, 173, 204, 298, 448, 567, 658, 688] [79, 174, 205, 299, 449, 568, 659, 689] [80, 175, 206, 300, 450, 569, 660, 690] [81, 176, 207, 301, 451, 570, 661, 691] [82, 177, 208, 302, 452, 571, 662, 692] [83, 178, 209, 303, 453, 572, 663, 693] [84, 179, 210, 304, 454, 573, 664, 694] [85, 180, 211, 305, 455, 574, 665, 695] [86, 181, 212, 306, 456, 575, 666, 696] [87, 182, 213, 307, 457, 576, 667, 697] [88, 183, 214, 308, 458, 577, 668, 698] [89, 184, 215, 309, 459, 578, 669, 699] [90, 185, 216, 310, 460, 579, 670, 700] [91, 186, 217, 311, 461, 580, 671, 701] [92, 187, 218, 312, 462, 581, 672, 702] [93, 188, 219, 313, 463, 485, 673, 703] [94, 189, 220, 314, 464, 486, 674, 704] [95, 190, 221, 315, 465, 487, 675, 705] [96, 191, 222, 316, 466, 488, 676, 706] [0, 192, 223, 317, 467, 489, 677, 707] [1, 193, 224, 318, 468, 490, 678, 708] [2, 97, 225, 319, 469, 491, 582, 709] [3, 98, 226, 320, 470, 492, 583, 710] [4, 99, 227, 321, 471, 493, 584, 711] [5, 100, 228, 322, 472, 494, 585, 712] [9, 149, 251, 330, 436, 565, 665, 698] [10, 150, 252, 331, 437, 566, 666, 699] [11, 151, 253, 332, 438, 567, 667, 700] [12, 152, 254, 333, 439, 568, 668, 701] [13, 153, 255, 334, 440, 569, 669, 702] [14, 154, 256, 335, 441, 570, 670, 703] [15, 155, 257, 336, 442, 571, 671, 704] [16, 156, 258, 337, 443, 572, 672, 705] [17, 157, 259, 338, 444, 573, 673, 706] [18, 158, 260, 339, 445, 574, 674, 707] [19, 159, 261, 340, 446, 575, 675, 708] [20, 160, 262, 341, 447, 576, 676, 709] [21, 161, 263, 342, 448, 577, 677, 710] [22, 162, 264, 343, 449, 578, 678, 711] [23, 163, 265, 344, 450, 579, 582, 712] [24, 164, 266, 345, 451, 580, 583, 713] [25, 165, 267, 346, 452, 581, 584, 714] [26, 166, 268, 347, 453, 485, 585, 715] [27, 167, 269, 348, 454, 486, 586, 716] [28, 168, 270, 349, 455, 487, 587, 717] [29, 169, 271, 350, 456, 488, 588, 718] [30, 170, 272, 351, 457, 489, 589, 719] [31, 171, 273, 352, 458, 490, 590, 720] [32, 172, 274, 353, 459, 491, 591, 721] [33, 173, 275, 354, 460, 492, 592, 722] [34, 174, 276, 355, 461, 493, 593, 723] [35, 175, 277, 356, 462, 494, 594, 724] [36, 176, 278, 357, 463, 495, 595, 725] [37, 177, 279, 358, 464, 496, 596, 726] [38, 178, 280, 359, 465, 497, 597, 727] [39, 179, 281, 360, 466, 498, 598, 728] [40, 180, 282, 361, 467, 499, 599, 729] [41, 181, 283, 362, 468, 500, 600, 730] [42, 182, 284, 363, 469, 501, 601, 731] [43, 183, 285, 364, 470, 502, 602, 732] [44, 184, 286, 365, 471, 503, 603, 733] [45, 185, 287, 366, 472, 504, 604, 734] [46, 186, 288, 367, 473, 505, 605, 735] [47, 187, 289, 368, 474, 506, 606, 736] [48, 188, 290, 369, 475, 507, 607, 737] [49, 189, 194, 370, 476, 508, 608, 738] [50, 190, 195, 371, 477, 509, 609, 739] [51, 191, 196, 372, 478, 510, 610, 740] [52, 192, 197, 373, 479, 511, 611, 741] [53, 193, 198, 374, 480, 512, 612, 742] [54, 97, 199, 375, 481, 513, 613, 743] [55, 98, 200, 376, 482, 514, 614, 744] [56, 99, 201, 377, 483, 515, 615, 745] [57, 100, 202, 378, 484, 516, 616, 746] [58, 101, 203, 379, 388, 517, 617, 747] [59, 102, 204, 380, 389, 518, 618, 748] [60, 103, 205, 381, 390, 519, 619, 749] [61, 104, 206, 382, 391, 520, 620, 750] [62, 105, 207, 383, 392, 521, 621, 751] [63, 106, 208, 384, 393, 522, 622, 752] [64, 107, 209, 385, 394, 523, 623, 753] [65, 108, 210, 386, 395, 524, 624, 754] [66, 109, 211, 387, 396, 525, 625, 755] [67, 110, 212, 291, 397, 526, 626, 756] [68, 111, 213, 292, 398, 527, 627, 757] [69, 112, 214, 293, 399, 528, 628, 758] [70, 113, 215, 294, 400, 529, 629, 759] [71, 114, 216, 295, 401, 530, 630, 760] [72, 115, 217, 296, 402, 531, 631, 761] [73, 116, 218, 297, 403, 532, 632, 762] [74, 117, 219, 298, 404, 533, 633, 763] [75, 118, 220, 299, 405, 534, 634, 764] [76, 119, 221, 300, 406, 535, 635, 765] [77, 120, 222, 301, 407, 536, 636, 766] [78, 121, 223, 302, 408, 537, 637, 767] [79, 122, 224, 303, 409, 538, 638, 768] [80, 123, 225, 304, 410, 539, 639, 769] [81, 124, 226, 305, 411, 540, 640, 770] [82, 125, 227, 306, 412, 541, 641, 771] [83, 126, 228, 307, 413, 542, 642, 772] [84, 127, 229, 308, 414, 543, 643, 773] [85, 128, 230, 309, 415, 544, 644, 774] [86, 129, 231, 310, 416, 545, 645, 775] [87, 130, 232, 311, 417, 546, 646, 679] [88, 131, 233, 312, 418, 547, 647, 680] [89, 132, 234, 313, 419, 548, 648, 681] [90, 133, 235, 314, 420, 549, 649, 682] [91, 134, 236, 315, 421, 550, 650, 683] [92, 135, 237, 316, 422, 551, 651, 684] [93, 136, 238, 317, 423, 552, 652, 685] [94, 137, 239, 318, 424, 553, 653, 686] [95, 138, 240, 319, 425, 554, 654, 687] [96, 139, 241, 320, 426, 555, 655, 688] [0, 140, 242, 321, 427, 556, 656, 689] [1, 141, 243, 322, 428, 557, 657, 690] [2, 142, 244, 323, 429, 558, 658, 691] [3, 143, 245, 324, 430, 559, 659, 692] [4, 144, 246, 325, 431, 560, 660, 693] [5, 145, 247, 326, 432, 561, 661, 694] [6, 146, 248, 327, 433, 562, 662, 695] [7, 147, 249, 328, 434, 563, 663, 696] [8, 148, 250, 329, 435, 564, 664, 697]
H_Z (291 checks, sparse supports)
[29, 143, 271, 368, 421, 559, 650, 736] [30, 144, 272, 369, 422, 560, 651, 737] [31, 145, 273, 370, 423, 561, 652, 738] [32, 146, 274, 371, 424, 562, 653, 739] [33, 147, 275, 372, 425, 563, 654, 740] [34, 148, 276, 373, 426, 564, 655, 741] [35, 149, 277, 374, 427, 565, 656, 742] [36, 150, 278, 375, 428, 566, 657, 743] [37, 151, 279, 376, 429, 567, 658, 744] [38, 152, 280, 377, 430, 568, 659, 745] [39, 153, 281, 378, 431, 569, 660, 746] [40, 154, 282, 379, 432, 570, 661, 747] [41, 155, 283, 380, 433, 571, 662, 748] [42, 156, 284, 381, 434, 572, 663, 749] [43, 157, 285, 382, 435, 573, 664, 750] [44, 158, 286, 383, 436, 574, 665, 751] [45, 159, 287, 384, 437, 575, 666, 752] [46, 160, 288, 385, 438, 576, 667, 753] [47, 161, 289, 386, 439, 577, 668, 754] [48, 162, 290, 387, 440, 578, 669, 755] [49, 163, 194, 291, 441, 579, 670, 756] [50, 164, 195, 292, 442, 580, 671, 757] [51, 165, 196, 293, 443, 581, 672, 758] [52, 166, 197, 294, 444, 485, 673, 759] [53, 167, 198, 295, 445, 486, 674, 760] [54, 168, 199, 296, 446, 487, 675, 761] [55, 169, 200, 297, 447, 488, 676, 762] [56, 170, 201, 298, 448, 489, 677, 763] [57, 171, 202, 299, 449, 490, 678, 764] [58, 172, 203, 300, 450, 491, 582, 765] [59, 173, 204, 301, 451, 492, 583, 766] [60, 174, 205, 302, 452, 493, 584, 767] [61, 175, 206, 303, 453, 494, 585, 768] [62, 176, 207, 304, 454, 495, 586, 769] [63, 177, 208, 305, 455, 496, 587, 770] [64, 178, 209, 306, 456, 497, 588, 771] [65, 179, 210, 307, 457, 498, 589, 772] [66, 180, 211, 308, 458, 499, 590, 773] [67, 181, 212, 309, 459, 500, 591, 774] [68, 182, 213, 310, 460, 501, 592, 775] [69, 183, 214, 311, 461, 502, 593, 679] [70, 184, 215, 312, 462, 503, 594, 680] [71, 185, 216, 313, 463, 504, 595, 681] [72, 186, 217, 314, 464, 505, 596, 682] [73, 187, 218, 315, 465, 506, 597, 683] [74, 188, 219, 316, 466, 507, 598, 684] [75, 189, 220, 317, 467, 508, 599, 685] [76, 190, 221, 318, 468, 509, 600, 686] [77, 191, 222, 319, 469, 510, 601, 687] [78, 192, 223, 320, 470, 511, 602, 688] [79, 193, 224, 321, 471, 512, 603, 689] [80, 97, 225, 322, 472, 513, 604, 690] [81, 98, 226, 323, 473, 514, 605, 691] [82, 99, 227, 324, 474, 515, 606, 692] [83, 100, 228, 325, 475, 516, 607, 693] [84, 101, 229, 326, 476, 517, 608, 694] [85, 102, 230, 327, 477, 518, 609, 695] [86, 103, 231, 328, 478, 519, 610, 696] [87, 104, 232, 329, 479, 520, 611, 697] [88, 105, 233, 330, 480, 521, 612, 698] [89, 106, 234, 331, 481, 522, 613, 699] [90, 107, 235, 332, 482, 523, 614, 700] [91, 108, 236, 333, 483, 524, 615, 701] [92, 109, 237, 334, 484, 525, 616, 702] [93, 110, 238, 335, 388, 526, 617, 703] [94, 111, 239, 336, 389, 527, 618, 704] [95, 112, 240, 337, 390, 528, 619, 705] [96, 113, 241, 338, 391, 529, 620, 706] [0, 114, 242, 339, 392, 530, 621, 707] [1, 115, 243, 340, 393, 531, 622, 708] [2, 116, 244, 341, 394, 532, 623, 709] [3, 117, 245, 342, 395, 533, 624, 710] [4, 118, 246, 343, 396, 534, 625, 711] [5, 119, 247, 344, 397, 535, 626, 712] [6, 120, 248, 345, 398, 536, 627, 713] [7, 121, 249, 346, 399, 537, 628, 714] [8, 122, 250, 347, 400, 538, 629, 715] [9, 123, 251, 348, 401, 539, 630, 716] [10, 124, 252, 349, 402, 540, 631, 717] [11, 125, 253, 350, 403, 541, 632, 718] [12, 126, 254, 351, 404, 542, 633, 719] [13, 127, 255, 352, 405, 543, 634, 720] [14, 128, 256, 353, 406, 544, 635, 721] [15, 129, 257, 354, 407, 545, 636, 722] [16, 130, 258, 355, 408, 546, 637, 723] [17, 131, 259, 356, 409, 547, 638, 724] [18, 132, 260, 357, 410, 548, 639, 725] [19, 133, 261, 358, 411, 549, 640, 726] [20, 134, 262, 359, 412, 550, 641, 727] [21, 135, 263, 360, 413, 551, 642, 728] [22, 136, 264, 361, 414, 552, 643, 729] [23, 137, 265, 362, 415, 553, 644, 730] [24, 138, 266, 363, 416, 554, 645, 731] [25, 139, 267, 364, 417, 555, 646, 732] [26, 140, 268, 365, 418, 556, 647, 733] [27, 141, 269, 366, 419, 557, 648, 734] [28, 142, 270, 367, 420, 558, 649, 735] [26, 103, 205, 387, 396, 559, 659, 715] [27, 104, 206, 291, 397, 560, 660, 716] [28, 105, 207, 292, 398, 561, 661, 717] [29, 106, 208, 293, 399, 562, 662, 718] [30, 107, 209, 294, 400, 563, 663, 719] [31, 108, 210, 295, 401, 564, 664, 720] [32, 109, 211, 296, 402, 565, 665, 721] [33, 110, 212, 297, 403, 566, 666, 722] [34, 111, 213, 298, 404, 567, 667, 723] [35, 112, 214, 299, 405, 568, 668, 724] [36, 113, 215, 300, 406, 569, 669, 725] [37, 114, 216, 301, 407, 570, 670, 726] [38, 115, 217, 302, 408, 571, 671, 727] [39, 116, 218, 303, 409, 572, 672, 728] [40, 117, 219, 304, 410, 573, 673, 729] [41, 118, 220, 305, 411, 574, 674, 730] [42, 119, 221, 306, 412, 575, 675, 731] [43, 120, 222, 307, 413, 576, 676, 732] [44, 121, 223, 308, 414, 577, 677, 733] [45, 122, 224, 309, 415, 578, 678, 734] [46, 123, 225, 310, 416, 579, 582, 735] [47, 124, 226, 311, 417, 580, 583, 736] [48, 125, 227, 312, 418, 581, 584, 737] [49, 126, 228, 313, 419, 485, 585, 738] [50, 127, 229, 314, 420, 486, 586, 739] [51, 128, 230, 315, 421, 487, 587, 740] [52, 129, 231, 316, 422, 488, 588, 741] [53, 130, 232, 317, 423, 489, 589, 742] [54, 131, 233, 318, 424, 490, 590, 743] [55, 132, 234, 319, 425, 491, 591, 744] [56, 133, 235, 320, 426, 492, 592, 745] [57, 134, 236, 321, 427, 493, 593, 746] [58, 135, 237, 322, 428, 494, 594, 747] [59, 136, 238, 323, 429, 495, 595, 748] [60, 137, 239, 324, 430, 496, 596, 749] [61, 138, 240, 325, 431, 497, 597, 750] [62, 139, 241, 326, 432, 498, 598, 751] [63, 140, 242, 327, 433, 499, 599, 752] [64, 141, 243, 328, 434, 500, 600, 753] [65, 142, 244, 329, 435, 501, 601, 754] [66, 143, 245, 330, 436, 502, 602, 755] [67, 144, 246, 331, 437, 503, 603, 756] [68, 145, 247, 332, 438, 504, 604, 757] [69, 146, 248, 333, 439, 505, 605, 758] [70, 147, 249, 334, 440, 506, 606, 759] [71, 148, 250, 335, 441, 507, 607, 760] [72, 149, 251, 336, 442, 508, 608, 761] [73, 150, 252, 337, 443, 509, 609, 762] [74, 151, 253, 338, 444, 510, 610, 763] [75, 152, 254, 339, 445, 511, 611, 764] [76, 153, 255, 340, 446, 512, 612, 765] [77, 154, 256, 341, 447, 513, 613, 766] [78, 155, 257, 342, 448, 514, 614, 767] [79, 156, 258, 343, 449, 515, 615, 768] [80, 157, 259, 344, 450, 516, 616, 769] [81, 158, 260, 345, 451, 517, 617, 770] [82, 159, 261, 346, 452, 518, 618, 771] [83, 160, 262, 347, 453, 519, 619, 772] [84, 161, 263, 348, 454, 520, 620, 773] [85, 162, 264, 349, 455, 521, 621, 774] [86, 163, 265, 350, 456, 522, 622, 775] [87, 164, 266, 351, 457, 523, 623, 679] [88, 165, 267, 352, 458, 524, 624, 680] [89, 166, 268, 353, 459, 525, 625, 681] [90, 167, 269, 354, 460, 526, 626, 682] [91, 168, 270, 355, 461, 527, 627, 683] [92, 169, 271, 356, 462, 528, 628, 684] [93, 170, 272, 357, 463, 529, 629, 685] [94, 171, 273, 358, 464, 530, 630, 686] [95, 172, 274, 359, 465, 531, 631, 687] [96, 173, 275, 360, 466, 532, 632, 688] [0, 174, 276, 361, 467, 533, 633, 689] [1, 175, 277, 362, 468, 534, 634, 690] [2, 176, 278, 363, 469, 535, 635, 691] [3, 177, 279, 364, 470, 536, 636, 692] [4, 178, 280, 365, 471, 537, 637, 693] [5, 179, 281, 366, 472, 538, 638, 694] [6, 180, 282, 367, 473, 539, 639, 695] [7, 181, 283, 368, 474, 540, 640, 696] [8, 182, 284, 369, 475, 541, 641, 697] [9, 183, 285, 370, 476, 542, 642, 698] [10, 184, 286, 371, 477, 543, 643, 699] [11, 185, 287, 372, 478, 544, 644, 700] [12, 186, 288, 373, 479, 545, 645, 701] [13, 187, 289, 374, 480, 546, 646, 702] [14, 188, 290, 375, 481, 547, 647, 703] [15, 189, 194, 376, 482, 548, 648, 704] [16, 190, 195, 377, 483, 549, 649, 705] [17, 191, 196, 378, 484, 550, 650, 706] [18, 192, 197, 379, 388, 551, 651, 707] [19, 193, 198, 380, 389, 552, 652, 708] [20, 97, 199, 381, 390, 553, 653, 709] [21, 98, 200, 382, 391, 554, 654, 710] [22, 99, 201, 383, 392, 555, 655, 711] [23, 100, 202, 384, 393, 556, 656, 712] [24, 101, 203, 385, 394, 557, 657, 713] [25, 102, 204, 386, 395, 558, 658, 714] [51, 104, 274, 360, 478, 498, 591, 750] [52, 105, 275, 361, 479, 499, 592, 751] [53, 106, 276, 362, 480, 500, 593, 752] [54, 107, 277, 363, 481, 501, 594, 753] [55, 108, 278, 364, 482, 502, 595, 754] [56, 109, 279, 365, 483, 503, 596, 755] [57, 110, 280, 366, 484, 504, 597, 756] [58, 111, 281, 367, 388, 505, 598, 757] [59, 112, 282, 368, 389, 506, 599, 758] [60, 113, 283, 369, 390, 507, 600, 759] [61, 114, 284, 370, 391, 508, 601, 760] [62, 115, 285, 371, 392, 509, 602, 761] [63, 116, 286, 372, 393, 510, 603, 762] [64, 117, 287, 373, 394, 511, 604, 763] [65, 118, 288, 374, 395, 512, 605, 764] [66, 119, 289, 375, 396, 513, 606, 765] [67, 120, 290, 376, 397, 514, 607, 766] [68, 121, 194, 377, 398, 515, 608, 767] [69, 122, 195, 378, 399, 516, 609, 768] [70, 123, 196, 379, 400, 517, 610, 769] [71, 124, 197, 380, 401, 518, 611, 770] [72, 125, 198, 381, 402, 519, 612, 771] [73, 126, 199, 382, 403, 520, 613, 772] [74, 127, 200, 383, 404, 521, 614, 773] [75, 128, 201, 384, 405, 522, 615, 774] [76, 129, 202, 385, 406, 523, 616, 775] [77, 130, 203, 386, 407, 524, 617, 679] [78, 131, 204, 387, 408, 525, 618, 680] [79, 132, 205, 291, 409, 526, 619, 681] [80, 133, 206, 292, 410, 527, 620, 682] [81, 134, 207, 293, 411, 528, 621, 683] [82, 135, 208, 294, 412, 529, 622, 684] [83, 136, 209, 295, 413, 530, 623, 685] [84, 137, 210, 296, 414, 531, 624, 686] [85, 138, 211, 297, 415, 532, 625, 687] [86, 139, 212, 298, 416, 533, 626, 688] [87, 140, 213, 299, 417, 534, 627, 689] [88, 141, 214, 300, 418, 535, 628, 690] [89, 142, 215, 301, 419, 536, 629, 691] [90, 143, 216, 302, 420, 537, 630, 692] [91, 144, 217, 303, 421, 538, 631, 693] [92, 145, 218, 304, 422, 539, 632, 694] [93, 146, 219, 305, 423, 540, 633, 695] [94, 147, 220, 306, 424, 541, 634, 696] [95, 148, 221, 307, 425, 542, 635, 697] [96, 149, 222, 308, 426, 543, 636, 698] [0, 150, 223, 309, 427, 544, 637, 699] [1, 151, 224, 310, 428, 545, 638, 700] [2, 152, 225, 311, 429, 546, 639, 701] [3, 153, 226, 312, 430, 547, 640, 702] [4, 154, 227, 313, 431, 548, 641, 703] [5, 155, 228, 314, 432, 549, 642, 704] [6, 156, 229, 315, 433, 550, 643, 705] [7, 157, 230, 316, 434, 551, 644, 706] [8, 158, 231, 317, 435, 552, 645, 707] [9, 159, 232, 318, 436, 553, 646, 708] [10, 160, 233, 319, 437, 554, 647, 709] [11, 161, 234, 320, 438, 555, 648, 710] [12, 162, 235, 321, 439, 556, 649, 711] [13, 163, 236, 322, 440, 557, 650, 712] [14, 164, 237, 323, 441, 558, 651, 713] [15, 165, 238, 324, 442, 559, 652, 714] [16, 166, 239, 325, 443, 560, 653, 715] [17, 167, 240, 326, 444, 561, 654, 716] [18, 168, 241, 327, 445, 562, 655, 717] [19, 169, 242, 328, 446, 563, 656, 718] [20, 170, 243, 329, 447, 564, 657, 719] [21, 171, 244, 330, 448, 565, 658, 720] [22, 172, 245, 331, 449, 566, 659, 721] [23, 173, 246, 332, 450, 567, 660, 722] [24, 174, 247, 333, 451, 568, 661, 723] [25, 175, 248, 334, 452, 569, 662, 724] [26, 176, 249, 335, 453, 570, 663, 725] [27, 177, 250, 336, 454, 571, 664, 726] [28, 178, 251, 337, 455, 572, 665, 727] [29, 179, 252, 338, 456, 573, 666, 728] [30, 180, 253, 339, 457, 574, 667, 729] [31, 181, 254, 340, 458, 575, 668, 730] [32, 182, 255, 341, 459, 576, 669, 731] [33, 183, 256, 342, 460, 577, 670, 732] [34, 184, 257, 343, 461, 578, 671, 733] [35, 185, 258, 344, 462, 579, 672, 734] [36, 186, 259, 345, 463, 580, 673, 735] [37, 187, 260, 346, 464, 581, 674, 736] [38, 188, 261, 347, 465, 485, 675, 737] [39, 189, 262, 348, 466, 486, 676, 738] [40, 190, 263, 349, 467, 487, 677, 739] [41, 191, 264, 350, 468, 488, 678, 740] [42, 192, 265, 351, 469, 489, 582, 741] [43, 193, 266, 352, 470, 490, 583, 742] [44, 97, 267, 353, 471, 491, 584, 743] [45, 98, 268, 354, 472, 492, 585, 744] [46, 99, 269, 355, 473, 493, 586, 745] [47, 100, 270, 356, 474, 494, 587, 746] [48, 101, 271, 357, 475, 495, 588, 747] [49, 102, 272, 358, 476, 496, 589, 748] [50, 103, 273, 359, 477, 497, 590, 749]
Code ID 776-198-20 · download JSON · raw on GitHub