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[[864,20,36]] d ≤
n
864
k
20
d
36
kd²/n
30.0
w
6
X/Z
1.11

Share this result

Distance

X/Z asymmetry 1.11 · d_X ≤ 36, 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 36 · witness weight 36 (claimed upper_bound)
witness found by @rajendrarajpurohit · verify/gate_changed.py (CI gate of PR #4477, orbit-fold search, seed 1516409015) · found at 1 trials · survived 1 trials · 2026-11-03
witness operator (support, 36 qubits)
[60, 62, 85, 90, 110, 119, 135, 144, 165, 168, 180, 184, 241, 243, 258, 276, 279, 282, 298, 301, 302, 330, 335, 336, 356, 357, 360, 361, 376, 381, 394, 396, 402, 410, 420, 427]
d_Z 40 · witness weight 40 (claimed upper_bound)
witness operator (support, 40 qubits)
[21, 96, 130, 229, 236, 255, 266, 282, 297, 305, 311, 329, 342, 354, 356, 377, 385, 395, 407, 413, 426, 441, 453, 478, 487, 501, 513, 528, 606, 632, 657, 680, 694, 706, 717, 719, 751, 754, 786, 836]
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 6 · H_Z 6
qubit degrees H_X 3 · H_Z 3
trapping sets H_X (1,3)×864 (2,4)×6480 (3,5)×64800 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 864 (2,4): 6480 (3,5): 64800 (3,7): 8640
trapping sets H_Z (1,3)×864 (2,4)×6480 (3,5)×64800 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 864 (2,4): 6480 (3,5): 64800 (3,7): 8640

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(648,720) (GAP SmallGroups id), H = <f5*f6*f7> = C3 given by generators in the polycyclic generating sequence f1,f2,... of G, m = [G:H] = 216, n = 4m = 864. 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*f5*f6*f7 + f1*f2*f32*f5*f7; B = [[1, 1 + f1*f32*f4*f52*f7], [1 + f1*f32*f4*f5*f7, f1*f32*f4*f52]]. Rebuild with gap/rebuild.g in https://github.com/rajendrarajpurohit/CLP_QLDPC.
model human (claimed, not verified)
builds on arXiv:2610.12782
date 2026-11-01
notes New parameter set, not in arXiv:2610.12782. Found by the paper's search procedure extended from m <= 100 to 120 <= m <= 250 (pairs (G,H) with H cyclic, core free, [G:N_G(H)] in {2,3,4}), weight 6 shape |a| = 3 with B entry weights 2 1 / 1 2 or 1 2 / 2 1. Screened with QDistRnd, 10^6 rounds per side; the witness here is from this tool's own RIS search. Authors Rajendra Rajpurohit, V. Lalitha, Shayan Srinivasa Garani. The CI gate of PR #4477 found a weight 36 logical (orbit-fold search); the claim was lowered from 40 to 36 and that witness is the one carried on that side.
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

[[864,20,36]] CLP code, check weight 6

Primary reference: arXiv:2610.12782, *Coset Lifted Product Codes*, Rajpurohit, Lalitha, Garani. This parameter set is not in the current version of the paper; it comes from the same search extended to longer codes and will appear in the updated version, with the data in https://github.com/rajendrarajpurohit/CLP_QLDPC (folder large_m/864_20_40).

Direction and hypothesis

The paper's search covered 120 <= n <= 400 (m = [G:H] from 30 to 100). The question was whether the same construction scales: does the 1x1 over 2x2 layout at check weight 6 keep its distance growing when m goes to 120 to 250, that is n from 480 to 1000, and where do such codes sit on this board's weight-6 frontier.

What was searched

25,240 pairs (G,H), H cyclic of order 2 to 9, core free, [G:N_G(H)] in {2,3,4}, [N_G(H):H] >= 4, from SmallGroups of order 240 to 2000 (orders with more than 2000 groups skipped). 1,500 random draws per pair of a with |a| = 3 and B with entry weights 2 1 / 1 2 or 1 2 / 2 1, then 20,000 draws per pair on the 6,836 pairs with 560 <= n <= 700 whose best k was at least 16, logging any draw whose (n, k, d) was not Pareto dominated by the weight-6 cell of this board on 24 Oct 2026. Screening ladder: 50 and 500 QDistRnd rounds with an early abort at the required distance, then 20,000, then 200,000 on both sides.

This code

G = SmallGroup(648,720), H = <f5*f6*f7> = C3, m = 216. a = 1 + f1*f3*f4*f5*f6*f7 + f1*f2*f3^2*f5*f7; B = [[1, 1 + f1*f3^2*f4*f5^2*f7], [1 + f1*f3^2*f4*f5*f7, f1*f3^2*f4*f5^2]].

Evidence trail

| stage | rounds / trials | result | |---|---|---| | search log | 200,000 QDistRnd per side | d <= 40 | | rescreen | 1,000,000 QDistRnd per side | d <= 40 | | this tool | 500,000 RIS trials per side | X <= 40, Z <= 40 |

The witnesses in the entry are the ones this tool found; each was checked by the verifier. Not certified exact; the paper's integer program certification does not reach these distances.

Dead ends

Shapes with |a| = 2 or |a| = 4 (B entry weights up to 2 2 / 2 2) raise k to 24 and far beyond at these lengths but over 9,560 pairs never paired that k with a distance above the frontier for its k. Bounds from the 200,000 round stage overestimate by 2 to 16 at n near 1000; only the 10^6 figures are reported.

Tools

GAP 4.15.1 with SmallGroups and QDistRnd, the construction and driver scripts of the repository above (large_m/search), no LLM in the search loop. Witness and verification: this repository's qldpc submit with --trials 500000.

Reproduction

gap/rebuild.g in the repository above, with G, H, a, B as given, rebuilds HX and HZ; verify.py there checks the structure and this board's verifier checks the witnesses.

Update after CI

The gate of PR #4477 (seed 1516409015, orbit-fold search) found a weight 36 logical. The claim is lowered to d <= 36 and that witness is carried in the entry. Our 10^6 round QDistRnd screen and the 500,000 trial RIS search had both stopped at 40.

Parity checks

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