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[[960,20,40]] d ≤
n
960
k
20
d
40
kd²/n
33.3333
w
6
X/Z
1.05

Share this result

Distance

X/Z asymmetry 1.05 · d_X ≤ 42, d_Z ≤ 40 · w_X = 6, w_Z = 6 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 42 · witness weight 42 (claimed upper_bound)
witness found by @rajendrarajpurohit · verify/gate_changed.py fast RIS, 8M trials, seed 6980315 · found at 1 trials · survived 1 trials · 2026-11-06
witness operator (support, 42 qubits)
[24, 42, 73, 85, 101, 140, 185, 218, 226, 264, 291, 298, 312, 325, 395, 458, 461, 463, 484, 522, 552, 585, 635, 723, 724, 738, 762, 763, 770, 774, 787, 837, 856, 860, 873, 889, 906, 923, 933, 944, 945, 953]
d_Z 40 · witness weight 40 (claimed upper_bound)
witness found by @rajendrarajpurohit · verify/heuristic_distance.py orbit-fold, 3000 trials, seed 1 · found at 1 trials · survived 1 trials · 2026-11-06
witness operator (support, 40 qubits)
[14, 39, 66, 109, 152, 191, 274, 277, 288, 297, 309, 314, 327, 338, 440, 454, 465, 472, 488, 508, 528, 545, 546, 567, 588, 589, 645, 682, 706, 717, 721, 729, 758, 785, 795, 828, 923, 946, 947, 957]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Diagnostics

computed by the verifier from the parity checks, the layout, and the stored witnesses; shown as evidence, not used for ranking
girth H_X 6 · H_Z 6 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 6 · H_Z 6
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×960 (2,4)×7200 (3,3)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 960 (2,4): 7200 (3,3): 24 (3,5): 71928 (3,7): 9600
trapping sets H_Z (1,3)×960 (2,4)×7200 (3,3)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 960 (2,4): 7200 (3,3): 24 (3,5): 71928 (3,7): 9600

Construction & provenance

authors @rajendrarajpurohit
provenance submitted through the challenge
novelty new parameter set claimed by submitter
construction Coset lifted product (CLP) code, Definition III.1 of arXiv:2610.12782, 1x1 over 2x2 layout, check weight 6. G = SmallGroup(480,1005) (GAP SmallGroups id), H = <f3> = C2 given by generators in the polycyclic generating sequence f1,f2,... of G, m = [G:H] = 240, n = 4m = 960. Protograph a over F_2[G] acts by the left coset action on G/H, protograph B over F_2[N_G(H)] by the right coset action. a = 1 + f1*f3*f4*f62*f74 + f1*f2*f3*f4*f62*f7; B = [[1 + f4*f5*f6*f73, 1], [1, f4*f5*f6 + f4*f6*f72]]. Rebuild with gap/rebuild.g in https://github.com/rajendrarajpurohit/CLP_QLDPC.
model human (claimed, not verified)
builds on arXiv:2610.12782
date 2026-11-06
notes Neighbour of the W6rest m = 240 family of arXiv:2610.12782 found by the entry-resampling walker (mut960 campaign, check weight 6, both sides screened at search time). Search-time QDistRnd bound d <= 56. This repository's fast RIS search at 8M trials (seed 6980315) found nothing below 42 on either side; the orbit-fold search (pynauty automorphisms) found weight 42 at 300 trials and a weight-40 Z-type logical at 3000 trials (seed 1), carried as the witness; 30000 fold trials found nothing lighter. The X side carries its weight-42 witness. Classical construction: a coset lifted product code in the framework of arXiv:2610.12782 (Definition III.1), obtained by the search procedure described in that paper over the GAP SmallGroups library. No AI model. No entry at check weight 6 with n <= 960 and k >= 20 reaches d = 40 on the current board.
family 2BGA coset (a tag, not a ranking)
locality unrestricted (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

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

[[960,20,40]]

[[960,20,40]] CLP code, check weight 6

Primary reference: arXiv:2610.12782, *Coset Lifted Product Codes*, Rajpurohit, Lalitha, Garani. Data and scripts: https://github.com/rajendrarajpurohit/CLP_QLDPC.

  • Search-time QDistRnd, 2 x 10^5 rounds per side: d <= 56.
  • This repository's fast RIS search, 8M trials, seed 6980315: nothing below 42 on either side; weight-42 X-type witness.
  • This repository's orbit-fold search (pynauty automorphisms): 42 at 300 trials; weight-40 Z-type logical at 3000 trials, seed 1, carried as the witness; 30000 trials find nothing lighter.
  • Classical construction: a coset lifted product code in the framework of arXiv:2610.12782 (Definition III.1), obtained by the search procedure described in that paper over the GAP SmallGroups library. No AI model.

Direction and hypothesis

Extension of the paper's search to m = 240 at check weight 6, followed by an entry-resampling walk around the best W6rest pair. The walk keeps the group pair and layout fixed and resamples one or two entries of the protographs per step; this code is a neighbour of the W6rest m = 240 family.

This code

G = SmallGroup(480,1005), H = <f3> = C2, m = 240, n = 4m = 960, check weight 6, 1x1 over 2x2 layout. a = 1 + f1*f3*f4*f6^2*f7^4 + f1*f2*f3*f4*f6^2*f7; B = [[1 + f4*f5*f6*f7^3, 1], [1, f4*f5*f6 + f4*f6*f7^2]].

Evidence trail

| stage | rounds / trials | result | |---|---|---| | search log | 2 x 10^5 QDistRnd per side | d <= 56 | | this tool, fast RIS | 8M trials, seed 6980315 | nothing below 42 on either side; weight-42 X witness | | this tool, orbit-fold | 300 / 3000 / 30000 trials | 42 / weight-40 Z witness / nothing lighter |

Not certified exact. The witnesses in the entry are the ones this tool found, checked by the verifier. [[960,20,40]] at check weight 6 has no dominator on the board; the nearest entry with k >= 20 at n <= 960 is [[960,24,38]].

Dead ends

The ten walker neighbours of the paper's [[864,20]] code all fold to 36 under the orbit-fold search, matching the board's entry; the m = 216 and m = 240 pair searches at K >= 20 produced four sieve survivors, all refuted at 2.5 x 10^5 RIS trials or by the orbit-fold.

Tools

GAP 4.15.1 with SmallGroups and QDistRnd, the construction and driver scripts of the repository above, no LLM in the search loop. Witness and verification: this repository's gate_changed.py RIS search and heuristic_distance.py orbit-fold.

Reproduction

gap/rebuild.g in the repository above, with G, H, a, B as given, rebuilds HX and HZ.

Parity checks

X-checks 480 (max weight 6) · Z-checks 480 (max weight 6)
H_X (480 checks, sparse supports)
[0, 146, 237, 480, 658, 720] [1, 82, 215, 481, 589, 721] [2, 155, 235, 482, 708, 722] [3, 149, 203, 483, 533, 723] [4, 185, 226, 484, 616, 724] [5, 100, 198, 485, 692, 725] [6, 196, 235, 486, 693, 726] [7, 91, 211, 487, 665, 727] [8, 123, 232, 488, 645, 728] [9, 126, 184, 489, 546, 729] [10, 42, 140, 490, 635, 730] [11, 138, 211, 491, 636, 731] [12, 71, 236, 492, 609, 732] [13, 111, 239, 493, 687, 733] [14, 109, 190, 494, 648, 734] [15, 188, 237, 495, 718, 735] [16, 105, 227, 496, 572, 736] [17, 103, 119, 497, 574, 737] [18, 117, 236, 498, 575, 738] [19, 144, 160, 499, 660, 739] [20, 158, 239, 500, 661, 740] [21, 57, 225, 501, 614, 741] [22, 110, 220, 502, 712, 742] [23, 108, 188, 503, 524, 743] [24, 132, 230, 504, 703, 744] [25, 52, 231, 505, 626, 745] [26, 50, 131, 506, 578, 746] [27, 129, 215, 507, 696, 747] [28, 166, 214, 508, 682, 748] [29, 77, 179, 509, 683, 749] [30, 177, 230, 490, 510, 750] [31, 80, 96, 511, 591, 751] [32, 94, 231, 512, 592, 752] [15, 33, 183, 513, 544, 753] [34, 51, 176, 514, 676, 754] [35, 49, 129, 515, 677, 755] [36, 114, 223, 516, 652, 756] [34, 37, 193, 517, 523, 757] [38, 191, 203, 518, 655, 758] [39, 66, 218, 519, 605, 759] [40, 216, 226, 520, 710, 760] [41, 64, 220, 521, 685, 761] [42, 101, 225, 522, 686, 762] [43, 99, 196, 523, 600, 763] [44, 61, 163, 524, 618, 764] [45, 161, 223, 525, 619, 765] [46, 59, 165, 503, 526, 766] [35, 47, 222, 527, 621, 767] [33, 48, 191, 528, 622, 768] [49, 98, 200, 529, 570, 769] [50, 67, 234, 530, 694, 770] [51, 65, 216, 497, 531, 771] [52, 156, 190, 532, 659, 772] [28, 53, 147, 533, 565, 773] [54, 99, 224, 534, 566, 774] [55, 88, 238, 535, 716, 775] [56, 86, 171, 536, 634, 776] [57, 169, 232, 537, 540, 777] [22, 58, 174, 537, 538, 778] [59, 172, 184, 539, 668, 779] [20, 60, 176, 540, 624, 780] [43, 61, 183, 541, 625, 781] [41, 62, 138, 542, 713, 782] [63, 121, 137, 543, 707, 783] [64, 135, 238, 511, 544, 784] [38, 65, 213, 545, 599, 785] [66, 87, 208, 513, 546, 786] [67, 85, 169, 514, 547, 787] [40, 68, 142, 510, 548, 788] [23, 69, 210, 549, 638, 789] [21, 70, 172, 550, 639, 790] [71, 92, 131, 551, 590, 791] [4, 72, 83, 552, 704, 792] [41, 73, 182, 553, 705, 793] [69, 74, 154, 554, 561, 794] [75, 152, 227, 555, 689, 795] [11, 76, 222, 556, 563, 796] [77, 104, 165, 557, 564, 797] [78, 102, 117, 558, 691, 798] [30, 79, 234, 559, 650, 799] [80, 145, 200, 560, 651, 800] [81, 143, 158, 556, 561, 801] [82, 147, 198, 562, 709, 802] [24, 83, 156, 516, 563, 803] [84, 108, 219, 564, 646, 804] [27, 85, 202, 531, 565, 805] [70, 86, 195, 566, 662, 806] [68, 87, 152, 567, 663, 807] [72, 88, 193, 534, 568, 808] [1, 89, 150, 569, 664, 809] [90, 102, 164, 485, 570, 810] [91, 112, 218, 571, 617, 811] [8, 92, 186, 526, 572, 812] [93, 143, 199, 527, 573, 813] [63, 94, 101, 496, 574, 814] [56, 95, 157, 575, 612, 815] [96, 155, 219, 576, 613, 816] [47, 97, 206, 577, 673, 817] [98, 204, 214, 578, 582, 818] [45, 99, 208, 579, 675, 819] [78, 100, 213, 487, 580, 820] [76, 101, 177, 581, 585, 821] [6, 102, 210, 580, 582, 822] [81, 103, 142, 581, 583, 823] [79, 94, 104, 584, 699, 824] [83, 105, 140, 585, 666, 825] [2, 92, 106, 586, 667, 826] [49, 107, 175, 587, 719, 827] [75, 108, 181, 588, 643, 828] [48, 109, 229, 548, 589, 829] [46, 110, 204, 549, 590, 830] [111, 133, 171, 481, 591, 831] [16, 112, 124, 551, 592, 832] [76, 113, 212, 552, 593, 833] [53, 114, 174, 547, 594, 834] [0, 115, 127, 595, 679, 835] [79, 116, 141, 596, 680, 836] [19, 43, 117, 597, 637, 837] [14, 93, 118, 598, 717, 838] [91, 119, 175, 543, 599, 839] [32, 120, 195, 600, 607, 840] [62, 121, 202, 601, 608, 841] [60, 122, 161, 602, 711, 842] [119, 123, 150, 603, 610, 843] [25, 72, 124, 604, 611, 844] [33, 125, 221, 521, 605, 845] [126, 160, 186, 606, 688, 846] [55, 112, 127, 492, 607, 847] [65, 128, 233, 603, 608, 848] [56, 110, 129, 554, 609, 849] [63, 130, 148, 555, 610, 850] [131, 146, 224, 611, 684, 851] [115, 132, 154, 573, 612, 852] [9, 106, 133, 613, 695, 853] [60, 134, 201, 499, 614, 854] [10, 104, 135, 576, 615, 855] [58, 73, 136, 501, 616, 856] [71, 137, 221, 502, 617, 857] [29, 138, 145, 483, 618, 858] [97, 113, 139, 568, 619, 859] [111, 140, 233, 569, 620, 860] [24, 141, 197, 525, 621, 861] [64, 142, 189, 622, 657, 862] [18, 143, 229, 623, 702, 863] [122, 144, 181, 505, 624, 864] [120, 135, 145, 625, 629, 865] [124, 146, 179, 506, 626, 866] [12, 133, 147, 507, 627, 867] [85, 148, 207, 628, 632, 868] [96, 127, 149, 627, 629, 869] [13, 53, 150, 628, 630, 870] [21, 151, 209, 631, 715, 871] [14, 51, 152, 632, 697, 872] [19, 84, 153, 633, 698, 873] [82, 154, 182, 623, 634, 874] [89, 155, 206, 489, 635, 875] [3, 156, 167, 594, 636, 876] [120, 157, 180, 595, 637, 877] [44, 78, 158, 491, 638, 878] [37, 134, 159, 597, 639, 879] [132, 160, 207, 598, 640, 880] [5, 81, 161, 593, 641, 881] [39, 54, 162, 642, 706, 882] [52, 163, 209, 509, 643, 883] [2, 139, 164, 644, 678, 884] [20, 130, 165, 588, 645, 885] [106, 163, 166, 646, 653, 886] [7, 115, 167, 647, 654, 887] [68, 168, 194, 559, 648, 888] [35, 58, 169, 649, 656, 889] [10, 151, 170, 482, 650, 890] [149, 164, 171, 562, 651, 891] [67, 97, 172, 517, 652, 892] [29, 173, 187, 518, 653, 893] [174, 185, 199, 649, 654, 894] [28, 175, 189, 601, 655, 895] [57, 176, 197, 602, 656, 896] [31, 62, 177, 620, 657, 897] [26, 116, 178, 529, 658, 898] [114, 179, 194, 530, 659, 899] [25, 118, 180, 480, 660, 900] [11, 181, 192, 532, 661, 901] [55, 159, 182, 498, 662, 902] [30, 183, 217, 615, 663, 903] [109, 148, 184, 567, 664, 904] [137, 167, 185, 538, 665, 905] [36, 89, 186, 539, 666, 906] [46, 187, 228, 667, 671, 907] [37, 87, 188, 541, 668, 908] [44, 125, 189, 542, 669, 909] [123, 190, 212, 670, 674, 910] [23, 39, 191, 669, 671, 911] [5, 128, 192, 670, 672, 912] [126, 141, 193, 579, 673, 913] [4, 130, 194, 674, 714, 914] [15, 139, 195, 535, 675, 915] [17, 122, 196, 512, 676, 916] [74, 90, 197, 641, 677, 917] [88, 198, 228, 642, 678, 918] [12, 178, 199, 515, 679, 919] [45, 170, 200, 644, 680, 920] [13, 95, 201, 640, 681, 921] [6, 173, 202, 545, 682, 922] [50, 84, 203, 508, 683, 923] [26, 70, 204, 684, 690, 924] [31, 107, 205, 493, 685, 925] [105, 201, 206, 606, 686, 926] [1, 192, 207, 494, 687, 927] [59, 118, 208, 495, 688, 928] [8, 209, 217, 557, 689, 929] [98, 159, 210, 558, 690, 930] [100, 157, 211, 647, 691, 931] [7, 162, 212, 484, 692, 932] [32, 153, 213, 571, 693, 933] [34, 151, 214, 486, 694, 934] [66, 187, 215, 528, 695, 935] [48, 74, 216, 583, 696, 936] [17, 168, 217, 584, 697, 937] [166, 180, 218, 698, 701, 938] [16, 170, 219, 586, 699, 939] [38, 178, 220, 587, 700, 940] [0, 173, 221, 700, 701, 941] [40, 95, 222, 504, 702, 942] [42, 93, 223, 577, 703, 943] [36, 136, 224, 550, 704, 944] [18, 205, 225, 681, 705, 945] [86, 125, 226, 553, 706, 946] [22, 128, 227, 488, 707, 947] [9, 153, 228, 519, 708, 948] [27, 162, 229, 520, 709, 949] [73, 103, 230, 522, 710, 950] [113, 144, 231, 604, 711, 951] [69, 107, 232, 500, 712, 952] [3, 205, 233, 630, 713, 953] [75, 136, 234, 631, 714, 954] [77, 134, 235, 633, 715, 955] [54, 80, 236, 536, 716, 956] [47, 168, 237, 596, 717, 957] [61, 116, 238, 560, 718, 958] [90, 121, 239, 672, 719, 959] [240, 386, 477, 480, 764, 809] [241, 322, 455, 481, 783, 920] [242, 395, 475, 482, 840, 889] [243, 389, 443, 483, 725, 859] [244, 425, 466, 484, 737, 853] [245, 340, 438, 485, 805, 855] [246, 436, 475, 486, 806, 856] [247, 331, 451, 487, 863, 955] [248, 363, 472, 488, 730, 789] [249, 366, 424, 489, 749, 945] [250, 282, 380, 490, 828, 946] [251, 378, 451, 491, 749, 829] [252, 311, 476, 492, 761, 929] [253, 351, 479, 493, 796, 924] [254, 349, 430, 494, 756, 798] [255, 428, 477, 495, 886, 927] [256, 345, 467, 496, 739, 815] [257, 343, 359, 497, 741, 902] [258, 357, 476, 498, 742, 903] [259, 384, 400, 499, 766, 897] [260, 398, 479, 500, 767, 898] [261, 297, 465, 501, 736, 768] [262, 350, 460, 502, 852, 900] [263, 348, 428, 503, 853, 901] [264, 372, 470, 504, 780, 869] [265, 292, 471, 505, 819, 959] [266, 290, 371, 506, 775, 910] [267, 369, 455, 507, 819, 905] [268, 406, 454, 508, 751, 754] [269, 317, 419, 509, 753, 834] [270, 417, 470, 510, 754, 835] [271, 320, 336, 511, 785, 957] [272, 334, 471, 512, 783, 786] [255, 273, 423, 513, 748, 880] [274, 291, 416, 514, 785, 875] [275, 289, 369, 515, 786, 876] [276, 354, 463, 516, 799, 895] [274, 277, 433, 517, 722, 848] [278, 431, 443, 518, 802, 951] [279, 306, 458, 519, 732, 842] [280, 456, 466, 520, 843, 948] [281, 304, 460, 521, 794, 844] [282, 341, 465, 522, 795, 845] [283, 339, 436, 523, 924, 950] [284, 301, 403, 524, 769, 861] [285, 401, 463, 525, 770, 862] [286, 299, 405, 526, 720, 813] [275, 287, 462, 527, 772, 935] [273, 288, 431, 528, 739, 773] [289, 338, 440, 529, 723, 807] [290, 307, 474, 530, 808, 932] [291, 305, 456, 531, 809, 933] [292, 396, 430, 532, 765, 810] [268, 293, 387, 533, 897, 934] [294, 339, 464, 534, 737, 898] [295, 328, 478, 535, 822, 825] [296, 326, 411, 536, 727, 779] [297, 409, 472, 537, 825, 911] [262, 298, 414, 538, 744, 938] [299, 412, 424, 539, 863, 866] [260, 300, 416, 540, 817, 940] [283, 301, 423, 541, 744, 818] [281, 302, 378, 542, 866, 936] [303, 361, 377, 543, 788, 791] [304, 375, 478, 544, 789, 792] [278, 305, 453, 545, 721, 752] [306, 327, 448, 546, 791, 881] [307, 325, 409, 547, 792, 882] [280, 308, 382, 548, 728, 918] [263, 309, 450, 549, 828, 831] [261, 310, 412, 550, 829, 832] [311, 332, 371, 551, 728, 784] [244, 312, 323, 552, 831, 916] [281, 313, 422, 553, 832, 917] [309, 314, 394, 554, 733, 804] [315, 392, 467, 555, 846, 931] [251, 316, 462, 556, 734, 893] [317, 344, 405, 557, 735, 894] [318, 342, 357, 558, 799, 849] [270, 319, 474, 559, 757, 887] [320, 385, 440, 560, 758, 888] [321, 383, 398, 561, 889, 958] [322, 387, 438, 562, 841, 890] [264, 323, 396, 563, 842, 891] [324, 348, 459, 564, 796, 948] [267, 325, 442, 565, 724, 774] [310, 326, 435, 566, 811, 904] [308, 327, 392, 567, 725, 812] [312, 328, 433, 568, 726, 860] [241, 329, 390, 569, 769, 814] [330, 342, 404, 570, 770, 815] [331, 352, 458, 571, 738, 854] [248, 332, 426, 572, 855, 952] [333, 383, 439, 573, 764, 856] [303, 334, 341, 574, 807, 857] [296, 335, 397, 575, 766, 932] [336, 395, 459, 576, 767, 933] [287, 337, 446, 577, 745, 747] [338, 444, 454, 578, 869, 872] [285, 339, 448, 579, 746, 823] [318, 340, 453, 580, 747, 824] [316, 341, 417, 581, 872, 941] [246, 342, 450, 582, 776, 954] [321, 343, 382, 583, 775, 777] [319, 334, 344, 584, 905, 908] [323, 345, 380, 585, 776, 864] [242, 332, 346, 586, 777, 865] [289, 347, 415, 587, 908, 953] [315, 348, 421, 588, 729, 731] [288, 349, 469, 589, 834, 837] [286, 350, 444, 590, 835, 838] [351, 373, 411, 591, 731, 790] [256, 352, 364, 592, 837, 921] [316, 353, 452, 593, 838, 922] [293, 354, 414, 594, 748, 750] [240, 355, 367, 595, 875, 878] [319, 356, 381, 596, 876, 879] [259, 283, 357, 597, 750, 830] [254, 333, 358, 598, 878, 944] [331, 359, 415, 599, 879, 945] [272, 360, 435, 600, 759, 850] [302, 361, 442, 601, 760, 851] [300, 362, 401, 602, 761, 892] [359, 363, 390, 603, 762, 930] [265, 312, 364, 604, 733, 763] [273, 365, 461, 605, 846, 895] [366, 400, 426, 606, 797, 925] [295, 352, 367, 607, 798, 926] [305, 368, 473, 608, 840, 927] [296, 350, 369, 609, 887, 928] [303, 370, 388, 610, 732, 888] [371, 386, 464, 611, 843, 958] [355, 372, 394, 612, 740, 816] [249, 346, 373, 613, 741, 858] [300, 374, 441, 614, 742, 859] [250, 344, 375, 615, 724, 743] [298, 313, 376, 616, 811, 861] [311, 377, 461, 617, 812, 862] [269, 378, 385, 618, 768, 899] [337, 353, 379, 619, 805, 900] [351, 380, 473, 620, 806, 901] [264, 381, 437, 621, 723, 854] [304, 382, 429, 622, 808, 952] [258, 383, 469, 623, 778, 781] [362, 384, 421, 624, 779, 782] [360, 375, 385, 625, 911, 914] [364, 386, 419, 626, 781, 870] [252, 373, 387, 627, 782, 871] [325, 388, 447, 628, 914, 956] [336, 367, 389, 629, 817, 820] [253, 293, 390, 630, 818, 821] [261, 391, 449, 631, 936, 939] [254, 291, 392, 632, 820, 906] [259, 324, 393, 633, 821, 907] [322, 394, 422, 634, 939, 959] [329, 395, 446, 635, 752, 755] [243, 396, 407, 636, 881, 884] [360, 397, 420, 637, 882, 885] [284, 318, 398, 638, 755, 836] [277, 374, 399, 639, 884, 947] [372, 400, 447, 640, 751, 885] [245, 321, 401, 641, 784, 787] [279, 294, 402, 642, 916, 919] [292, 403, 449, 643, 917, 920] [242, 379, 404, 644, 787, 877] [260, 370, 405, 645, 919, 957] [346, 403, 406, 646, 800, 896] [247, 355, 407, 647, 722, 801] [308, 408, 434, 648, 802, 929] [275, 298, 409, 649, 759, 803] [250, 391, 410, 650, 760, 804] [389, 404, 411, 651, 892, 931] [307, 337, 412, 652, 844, 949] [269, 413, 427, 653, 756, 845] [414, 425, 439, 654, 886, 950] [268, 415, 429, 655, 757, 925] [297, 416, 437, 656, 758, 926] [271, 302, 417, 657, 720, 771] [266, 356, 418, 658, 772, 902] [354, 419, 434, 659, 773, 903] [265, 358, 420, 660, 740, 774] [251, 421, 432, 661, 858, 904] [295, 399, 422, 662, 736, 810] [270, 423, 457, 663, 852, 934] [349, 388, 424, 664, 738, 899] [377, 407, 425, 665, 823, 826] [276, 329, 426, 666, 824, 827] [286, 427, 468, 667, 941, 943] [277, 327, 428, 668, 826, 912] [284, 365, 429, 669, 827, 913] [363, 430, 452, 670, 822, 943] [263, 279, 431, 671, 864, 867] [245, 368, 432, 672, 865, 868] [366, 381, 433, 673, 953, 955] [244, 370, 434, 674, 867, 937] [255, 379, 435, 675, 868, 938] [257, 362, 436, 676, 790, 793] [314, 330, 437, 677, 921, 923] [328, 438, 468, 678, 730, 922] [252, 418, 439, 679, 793, 883] [285, 410, 440, 680, 788, 923] [253, 335, 441, 681, 830, 833] [246, 413, 442, 682, 944, 946] [290, 324, 443, 683, 833, 918] [266, 310, 444, 684, 734, 847] [271, 347, 445, 685, 735, 848] [345, 441, 446, 686, 849, 951] [241, 432, 447, 687, 800, 850] [299, 358, 448, 688, 801, 851] [248, 449, 457, 689, 794, 890] [338, 399, 450, 690, 795, 891] [340, 397, 451, 691, 797, 949] [247, 402, 452, 692, 726, 813] [272, 393, 453, 693, 814, 935] [274, 391, 454, 694, 771, 816] [306, 427, 455, 695, 765, 857] [288, 314, 456, 696, 870, 873] [257, 408, 457, 697, 871, 874] [406, 420, 458, 698, 780, 956] [256, 410, 459, 699, 873, 942] [278, 418, 460, 700, 745, 874] [240, 413, 461, 701, 906, 909] [280, 335, 462, 702, 907, 910] [282, 333, 463, 703, 909, 954] [276, 376, 464, 704, 836, 839] [258, 445, 465, 705, 753, 947] [326, 365, 466, 706, 729, 839] [262, 368, 467, 707, 877, 880] [249, 393, 468, 708, 762, 893] [267, 402, 469, 709, 763, 894] [313, 343, 470, 710, 847, 896] [353, 384, 471, 711, 841, 928] [309, 347, 472, 712, 743, 860] [243, 445, 473, 713, 912, 915] [315, 376, 474, 714, 727, 913] [317, 374, 475, 715, 778, 915] [294, 320, 476, 716, 937, 940] [287, 408, 477, 717, 721, 883] [301, 356, 478, 718, 803, 930] [330, 361, 479, 719, 746, 942]
H_Z (480 checks, sparse supports)
[0, 180, 240, 480, 595, 701] [1, 111, 241, 481, 569, 687] [2, 170, 242, 482, 586, 644] [3, 138, 243, 483, 636, 713] [4, 212, 244, 484, 552, 674] [5, 90, 245, 485, 641, 672] [6, 214, 246, 486, 582, 682] [7, 100, 247, 487, 647, 692] [8, 227, 248, 488, 572, 689] [9, 155, 249, 489, 613, 708] [10, 30, 250, 490, 615, 650] [11, 158, 251, 491, 556, 661] [12, 127, 252, 492, 627, 679] [13, 205, 253, 493, 630, 681] [14, 207, 254, 494, 598, 632] [15, 208, 255, 495, 513, 675] [16, 94, 256, 496, 592, 699] [17, 51, 257, 497, 676, 697] [18, 182, 258, 498, 623, 705] [19, 134, 259, 499, 597, 633] [20, 232, 260, 500, 540, 645] [21, 136, 261, 501, 550, 631] [22, 137, 262, 502, 538, 707] [23, 46, 263, 503, 549, 671] [24, 222, 264, 504, 563, 621] [25, 144, 265, 505, 604, 660] [26, 146, 266, 506, 658, 684] [27, 147, 267, 507, 565, 709] [28, 203, 268, 508, 533, 655] [29, 163, 269, 509, 618, 653] [30, 68, 270, 510, 559, 663] [31, 64, 271, 511, 657, 685] [32, 196, 272, 512, 600, 693] [33, 66, 273, 513, 528, 605] [34, 67, 274, 514, 517, 694] [35, 199, 275, 515, 527, 649] [36, 83, 276, 516, 666, 704] [37, 172, 277, 517, 639, 668] [38, 173, 278, 518, 545, 700] [39, 228, 279, 519, 642, 671] [40, 229, 280, 520, 548, 702] [41, 125, 281, 521, 542, 553] [42, 230, 282, 490, 522, 703] [37, 43, 283, 523, 541, 597] [23, 44, 284, 524, 638, 669] [45, 141, 285, 525, 579, 680] [46, 92, 286, 526, 590, 667] [47, 93, 287, 527, 577, 717] [48, 215, 288, 528, 589, 696] [49, 178, 289, 515, 529, 587] [50, 179, 290, 506, 530, 683] [51, 85, 291, 514, 531, 632] [52, 181, 292, 505, 532, 643] [3, 53, 293, 533, 594, 630] [54, 88, 294, 534, 642, 716] [55, 195, 295, 535, 607, 662] [56, 236, 296, 536, 575, 609] [57, 58, 297, 501, 537, 656] [58, 185, 298, 538, 616, 649] [59, 186, 299, 526, 539, 688] [57, 60, 300, 540, 602, 614] [61, 188, 301, 524, 541, 718] [62, 189, 302, 542, 601, 657] [63, 119, 303, 543, 574, 610] [33, 64, 304, 521, 544, 622] [65, 202, 305, 531, 545, 608] [9, 66, 306, 519, 546, 695] [67, 114, 307, 530, 547, 652] [68, 109, 308, 548, 567, 648] [69, 110, 309, 549, 554, 712] [70, 224, 310, 550, 566, 684] [71, 112, 311, 492, 551, 617] [72, 113, 312, 552, 568, 604] [73, 226, 313, 553, 616, 710] [74, 129, 314, 554, 677, 696] [75, 130, 315, 555, 588, 714] [76, 81, 316, 556, 581, 593] [77, 209, 317, 509, 557, 715] [78, 210, 318, 558, 580, 638] [79, 168, 319, 559, 584, 596] [80, 238, 320, 511, 560, 716] [74, 81, 321, 561, 583, 641] [82, 171, 322, 481, 562, 634] [76, 83, 323, 552, 563, 585] [77, 84, 324, 564, 633, 683] [53, 85, 325, 547, 565, 628] [54, 86, 326, 536, 566, 706] [87, 184, 327, 546, 567, 668] [88, 139, 328, 535, 568, 678] [89, 140, 329, 569, 635, 666] [49, 90, 330, 570, 677, 719] [91, 213, 331, 487, 571, 599] [16, 92, 332, 551, 572, 586] [93, 132, 333, 573, 598, 703] [17, 94, 334, 512, 574, 584] [18, 95, 335, 575, 681, 702] [96, 135, 336, 511, 576, 629] [97, 223, 337, 577, 619, 652] [26, 98, 338, 529, 578, 690] [99, 193, 339, 523, 534, 579] [100, 102, 340, 485, 580, 691] [101, 103, 341, 522, 574, 581] [98, 102, 342, 558, 570, 582] [103, 216, 343, 497, 583, 710] [104, 217, 344, 557, 584, 615] [101, 105, 345, 496, 585, 686] [106, 219, 346, 586, 613, 646] [107, 220, 347, 587, 685, 712] [108, 165, 348, 503, 564, 588] [1, 109, 349, 494, 589, 664] [71, 110, 350, 502, 590, 609] [31, 111, 351, 493, 591, 620] [32, 112, 352, 571, 592, 607] [113, 161, 353, 593, 619, 711] [114, 156, 354, 516, 594, 659] [115, 157, 355, 595, 612, 647] [116, 237, 356, 596, 658, 718] [117, 159, 357, 498, 558, 597] [118, 160, 358, 598, 660, 688] [65, 119, 359, 497, 599, 603] [43, 120, 360, 600, 625, 637] [121, 175, 361, 543, 601, 719] [122, 176, 362, 602, 624, 676] [123, 128, 363, 488, 603, 670] [124, 231, 364, 592, 604, 626] [39, 125, 365, 605, 669, 706] [126, 206, 366, 489, 606, 673] [120, 127, 367, 595, 607, 629] [121, 128, 368, 608, 672, 707] [12, 129, 369, 507, 515, 609] [123, 130, 370, 610, 645, 674] [124, 131, 371, 506, 551, 611] [95, 132, 372, 504, 612, 640] [96, 133, 373, 591, 613, 627] [21, 134, 374, 614, 639, 715] [135, 183, 375, 544, 615, 625] [4, 136, 376, 616, 704, 714] [91, 137, 377, 543, 617, 665] [44, 138, 378, 491, 542, 618] [45, 139, 379, 619, 644, 675] [140, 177, 380, 490, 585, 620] [47, 141, 381, 596, 621, 673] [48, 142, 382, 548, 583, 622] [143, 154, 383, 561, 573, 623] [60, 144, 384, 499, 624, 711] [61, 145, 385, 560, 618, 625] [25, 146, 386, 480, 611, 626] [147, 149, 387, 533, 562, 627] [148, 150, 388, 610, 628, 664] [145, 149, 389, 483, 629, 651] [150, 233, 390, 569, 603, 630] [151, 234, 391, 631, 650, 694] [148, 152, 392, 555, 567, 632] [153, 235, 393, 633, 693, 708] [56, 154, 394, 554, 612, 634] [10, 155, 395, 482, 576, 635] [11, 156, 396, 532, 563, 636] [117, 157, 397, 575, 637, 691] [69, 158, 398, 500, 561, 638] [70, 159, 399, 639, 662, 690] [160, 201, 400, 499, 606, 640] [161, 197, 401, 525, 602, 641] [162, 198, 402, 642, 692, 709] [108, 163, 403, 524, 643, 646] [164, 200, 404, 570, 644, 651] [8, 165, 405, 526, 557, 645] [84, 166, 406, 508, 646, 698] [167, 211, 407, 636, 647, 665] [14, 168, 408, 648, 697, 717] [169, 174, 409, 537, 547, 649] [79, 170, 410, 650, 680, 699] [80, 171, 411, 536, 591, 651] [36, 172, 412, 539, 550, 652] [166, 173, 413, 653, 682, 701] [167, 174, 414, 538, 594, 654] [38, 175, 415, 587, 599, 655] [169, 176, 416, 514, 540, 656] [142, 177, 417, 510, 581, 657] [0, 178, 418, 658, 679, 700] [52, 179, 419, 509, 626, 659] [19, 180, 420, 637, 660, 698] [20, 181, 421, 588, 624, 661] [86, 182, 422, 553, 634, 662] [87, 183, 423, 513, 541, 663] [89, 184, 424, 489, 539, 664] [7, 185, 425, 484, 654, 665] [105, 186, 426, 572, 606, 666] [106, 187, 427, 653, 667, 695] [59, 188, 428, 495, 503, 668] [189, 191, 429, 622, 655, 669] [190, 192, 430, 494, 532, 670] [187, 191, 431, 518, 528, 671] [192, 239, 432, 661, 672, 687] [97, 193, 433, 517, 568, 673] [190, 194, 434, 648, 659, 674] [99, 195, 435, 566, 600, 675] [34, 196, 436, 486, 523, 676] [35, 197, 437, 621, 656, 677] [164, 198, 438, 485, 562, 678] [115, 199, 439, 573, 654, 679] [116, 200, 440, 529, 560, 680] [201, 225, 441, 614, 681, 686] [28, 202, 442, 565, 601, 682] [29, 203, 443, 483, 518, 683] [131, 204, 444, 578, 590, 684] [41, 205, 445, 685, 705, 713] [42, 206, 446, 577, 635, 686] [13, 207, 447, 628, 640, 687] [126, 208, 448, 546, 579, 688] [75, 209, 449, 631, 643, 689] [204, 210, 450, 549, 582, 690] [78, 211, 451, 487, 491, 691] [5, 212, 452, 593, 670, 692] [6, 213, 453, 545, 580, 693] [50, 214, 454, 508, 578, 694] [133, 215, 455, 481, 507, 695] [27, 216, 456, 520, 531, 696] [152, 217, 457, 663, 689, 697] [153, 218, 458, 519, 571, 698] [104, 219, 459, 564, 576, 699] [220, 221, 460, 502, 521, 700] [218, 221, 461, 605, 617, 701] [143, 222, 462, 527, 556, 702] [24, 223, 463, 516, 525, 703] [72, 224, 464, 534, 611, 704] [73, 225, 465, 501, 522, 705] [162, 226, 466, 484, 520, 706] [63, 227, 467, 496, 555, 707] [2, 228, 468, 667, 678, 708] [82, 229, 469, 589, 623, 709] [40, 230, 470, 504, 510, 710] [122, 231, 471, 505, 512, 711] [22, 232, 472, 488, 537, 712] [62, 233, 473, 608, 620, 713] [194, 234, 474, 530, 559, 714] [151, 235, 475, 482, 486, 715] [55, 236, 476, 492, 498, 716] [118, 237, 477, 480, 495, 717] [15, 238, 478, 535, 544, 718] [107, 239, 479, 493, 500, 719] [0, 286, 417, 720, 835, 941] [1, 305, 477, 721, 809, 927] [2, 277, 407, 722, 826, 884] [3, 289, 381, 723, 876, 953] [4, 325, 375, 724, 792, 914] [5, 243, 327, 725, 881, 912] [6, 328, 452, 726, 822, 922] [7, 296, 474, 727, 887, 932] [8, 308, 311, 728, 812, 929] [9, 348, 466, 729, 853, 948] [10, 248, 438, 730, 855, 890] [11, 348, 351, 731, 796, 901] [12, 279, 370, 732, 867, 919] [13, 314, 364, 733, 870, 921] [14, 316, 444, 734, 838, 872] [15, 317, 445, 735, 753, 915] [16, 261, 422, 736, 832, 939] [17, 244, 294, 737, 916, 937] [18, 331, 424, 738, 863, 945] [19, 256, 288, 739, 837, 873] [20, 372, 420, 740, 780, 885] [21, 257, 373, 741, 790, 871] [22, 258, 374, 742, 778, 947] [23, 375, 472, 743, 789, 911] [24, 298, 301, 744, 803, 861] [25, 337, 460, 745, 844, 900] [26, 339, 479, 746, 898, 924] [27, 337, 340, 747, 805, 949] [28, 273, 354, 748, 773, 895] [29, 249, 251, 749, 858, 893] [30, 354, 357, 750, 799, 903] [31, 268, 400, 751, 897, 925] [32, 305, 395, 752, 840, 933] [33, 269, 465, 753, 768, 845] [34, 268, 270, 754, 757, 934] [35, 395, 398, 755, 767, 889] [36, 254, 413, 756, 906, 944] [37, 319, 415, 757, 879, 908] [38, 320, 416, 758, 785, 940] [39, 360, 409, 759, 882, 911] [40, 361, 410, 760, 788, 942] [41, 252, 362, 761, 782, 793] [42, 363, 468, 730, 762, 943] [43, 364, 469, 763, 781, 837] [44, 240, 333, 764, 878, 909] [45, 292, 455, 765, 819, 920] [46, 259, 335, 766, 830, 907] [47, 260, 336, 767, 817, 957] [48, 261, 378, 768, 829, 936] [49, 284, 329, 755, 769, 827] [50, 285, 330, 746, 770, 923] [51, 417, 454, 754, 771, 872] [52, 287, 418, 745, 772, 883] [53, 288, 419, 773, 834, 870] [54, 325, 420, 774, 882, 956] [55, 266, 343, 775, 847, 902] [56, 342, 345, 776, 815, 849] [57, 343, 346, 741, 777, 896] [58, 383, 475, 778, 856, 889] [59, 296, 384, 766, 779, 928] [60, 264, 458, 780, 842, 854] [61, 383, 386, 764, 781, 958] [62, 384, 387, 782, 841, 897] [63, 241, 272, 783, 814, 850] [64, 311, 401, 761, 784, 862] [65, 271, 274, 771, 785, 848] [66, 272, 275, 759, 786, 935] [67, 401, 404, 770, 787, 892] [68, 303, 440, 788, 807, 888] [69, 248, 304, 789, 794, 952] [70, 351, 436, 790, 806, 924] [71, 303, 306, 732, 791, 857] [72, 304, 307, 792, 808, 844] [73, 436, 439, 793, 856, 950] [74, 281, 449, 794, 917, 936] [75, 282, 450, 795, 828, 954] [76, 253, 324, 796, 821, 833] [77, 366, 451, 749, 797, 955] [78, 254, 367, 798, 820, 878] [79, 276, 318, 799, 824, 836] [80, 406, 447, 751, 800, 956] [81, 407, 448, 801, 823, 881] [82, 278, 408, 721, 802, 874] [83, 409, 478, 792, 803, 825] [84, 314, 410, 804, 873, 923] [85, 245, 379, 787, 805, 868] [86, 246, 380, 776, 806, 946] [87, 289, 334, 786, 807, 908] [88, 290, 382, 775, 808, 918] [89, 240, 291, 809, 875, 906] [90, 292, 422, 810, 917, 959] [91, 326, 376, 727, 811, 839] [92, 327, 377, 791, 812, 826] [93, 286, 452, 813, 838, 943] [94, 329, 453, 752, 814, 824] [95, 256, 330, 815, 921, 942] [96, 372, 454, 751, 816, 869] [97, 300, 389, 817, 859, 892] [98, 301, 390, 769, 818, 930] [99, 265, 267, 763, 774, 819] [100, 389, 392, 725, 820, 931] [101, 390, 393, 762, 814, 821] [102, 295, 430, 798, 810, 822] [103, 339, 425, 737, 823, 950] [104, 340, 426, 797, 824, 855] [105, 295, 297, 736, 825, 926] [106, 425, 428, 826, 853, 886] [107, 426, 429, 827, 925, 952] [108, 250, 309, 743, 804, 828] [109, 251, 310, 734, 829, 904] [110, 357, 441, 742, 830, 849] [111, 309, 312, 733, 831, 860] [112, 310, 313, 811, 832, 847] [113, 441, 443, 833, 859, 951] [114, 269, 349, 756, 834, 899] [115, 270, 350, 835, 852, 887] [116, 398, 464, 836, 898, 958] [117, 349, 352, 738, 798, 837] [118, 350, 353, 838, 900, 928] [119, 464, 466, 737, 839, 843] [120, 242, 368, 840, 865, 877] [121, 322, 471, 783, 841, 959] [122, 279, 323, 842, 864, 916] [123, 280, 371, 728, 843, 910] [124, 281, 412, 832, 844, 866] [125, 282, 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Code ID 960-20-40 · download JSON · raw on GitHub