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[[976,250,22]] d ≤
n
976
k
250
d
22
kd²/n
123.975
w
8
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 22, d_Z ≤ 22 · 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 22 · witness weight 22 (claimed upper_bound)
witness found by @MicheldeMessieres · Stern ISD (own C++), numpy-checked; survived 2M board gf2_fast RIS · found at 7×104 trials · survived 2×106 trials · 2026-10-14
witness operator (support, 22 qubits)
[13, 64, 105, 126, 236, 248, 252, 255, 377, 456, 511, 578, 602, 633, 642, 740, 745, 819, 886, 918, 941, 959]
d_Z 22 · witness weight 22 (claimed upper_bound)
witness found by @MicheldeMessieres · Stern ISD (own C++), numpy-checked; survived 2M board gf2_fast RIS · found at 7.7×104 trials · survived 2×106 trials · 2026-10-14
witness operator (support, 22 qubits)
[54, 99, 168, 228, 251, 279, 302, 325, 374, 434, 439, 485, 493, 542, 668, 730, 744, 767, 880, 908, 910, 922]
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)×976 (2,4)×10248 (3,5)×143472 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 976 (2,4): 10248 (3,5): 143472 (3,7): 20496
trapping sets H_Z (1,3)×976 (2,4)×10248 (3,5)×143472 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 976 (2,4): 10248 (3,5): 143472 (3,7): 20496

Construction & provenance

authors @MicheldeMessieres
provenance submitted through the challenge
novelty novelty not audited
construction Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), even cyclic lift P=122 (Z_122), n=8P=976, k=2P+6=250. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_122: E_x = [[0, 73, 60, 121, 0, 121, 60, 73], [0, 10, 10, 94, 94, 104, 104, 0], [0, 53, 0, 103, 46, 53, 46, 103]], E_z = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 113, 60, 29, 94, 39, 32, 103], [0, 23, 10, 45, 46, 117, 56, 73]]. The arrays solve the joint design system E_x[i][j] - E_x[i][j'] - E_z[i'][j] + E_z[i'][j'] = 0 (mod 122) 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) (the matchings of the board's [[904,230,22]] by @vprusso); girth 8 (no 4- or 6-cycles in either exponent array). On the even ring Z_122 the rank of H_X, H_Z depends on the exponents mod 2: the free exponents of the design system were restricted to one parity class in which rank H_X = rank H_Z = 363, so k = 2P+6 instead of the generic 2P+4, and the solution was annealed inside that class to reduce the number of 8-cycles. Same construction and design system as the board's [[904,230,22]], [[776,198,20]], [[712,182,20]], [[664,170,18]], [[632,162,18]] (@vprusso), [[808,206,20]] (@pandey-tushar), [[824,210,20]], [[792,202,20]], [[840,214,20]], [[856,218,20]], [[872,222,18]], [[888,226,18]] (@MathysRennela), [[568,146,18]] (@nihoniumqc) and the published [[584,150,18]] (Okada-Kasai).
model Claude Claude Opus 5.5 (Claude Code) (claimed, not verified)
builds on arXiv:2607.14091, arXiv:2610.06749, arXiv:2111.03654, arXiv:quant-ph/0701020, https://github.com/kasaikenta/pair-partition-cpm-css-codes
date 2026-10-14
notes Our contribution: the observation, in our own draws, that on the even ring Z_122 the number of logical qubits depends on the exponents mod 2; the choice of one parity class of the free design-system exponents in which k = 2P + 6 = 250 (two more than the generic 2P + 4); this draw from the 8-cycle-annealed solutions in that class; and the distance screening described in notes/976-250-22.md. The rank of a quasi-cyclic check matrix is set by its common factors with x^P - 1, which has repeated factors over GF(2) when P is even (x^122 - 1 = (x^61 - 1)^2), so extra logical qubits at even lifts are not claimed as a new effect; we found no (3,8) pair-partition CPM entry with k > 2P + 4 in the board's codes, notes and fieldnotes, and did not search the wider literature. Construction and design system: Okada and Kasai, arXiv:2607.14091 (quasi-cyclic CSS LDPC codes from circulant permutation matrices go back to Hagiwara and Imai, arXiv:quant-ph/0701020; @vprusso's entries also cite the lifted-product construction of Panteleev and Kalachev, arXiv:2111.03654). The matchings M0, M1, M2 are the same as in the cell's leader codes/904-230-22.json by @vprusso (found with Claude Fable 5.1); the (3,8) pattern at large lifts and the polishing of the 8-cycle count follow codes/904-230-22.json and codes/712-182-20.json by @vprusso; lifts beyond the paper's P = 73 start with codes/632-162-18.json by @vprusso; the girth-8 hard filter follows codes/808-206-20.json by @pandey-tushar; the score formula kd^2/n = d^2 (1/4 + 1/(2P)) at k = 2P + 4 and the lift cap are from fieldnotes/2026-09-20-screening-traps-at-n-900.md by @e-eight. Other (3,8) weight-8 entries of this family: codes/776-198-20.json and codes/664-170-18.json by @vprusso; codes/824-210-20.json, codes/792-202-20.json, codes/840-214-20.json, codes/856-218-20.json, codes/872-222-18.json and codes/888-226-18.json by @MathysRennela; codes/568-146-18.json by @nihoniumqc; and the published codes/584-150-18.json (Okada-Kasai). Even lifts are already on the board: P = 32 and P = 72 in codes/256-68-12.json and codes/576-148-18.json by @MathysRennela (arrays printed in Maskara et al., arXiv:2610.06749), both at k = 2P + 4. Exact search tool: cpm_distance by Okada and Kasai (github.com/kasaikenta/pair-partition-cpm-css-codes, MIT licence), run from a copy with two small patches of ours: the quasi-cyclic shortcut of one search root per base column, which the original enables only for prime P, enabled for composite P (any lifted word can be cyclically shifted so that its smallest index lies in the copy g = 0 of its base column), and a split option that divides the top-level branches of one root into disjoint pieces. Every logical of this family has even weight (noted in codes/904-230-22.json). Distance is a witness-backed upper bound (confidence upper_bound): the patched cpm_distance, run to completion in 29 pieces per side, found no non-trivial logical of weight 20 or less on either side (3005 CPU-s X, 4698 CPU-s Z), so with even weights d = 22 if the tool and our patch are correct; this was not checked by the board's certifier, and the piece logs are available on request. Heuristic searches found nothing lighter than 22: 2000000 board gf2_fast RIS trials per side (pair depth 8) and Stern information-set decoding, 6 runs of 590 s per side on fresh seeds. Literature novelty is unverified.
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

[[976,250,22]] — pair-partition CPM (3,8) code at the even lift P = 122, with k = 2P + 6

Direction & hypothesis

Cell: CSS, unrestricted, weight-8, extended tier (n <= 1000 with w <= 8 and d <= 40). In the (3,8) pair-partition CPM family of Okada and Kasai (arXiv:2607.14091) n = 8P and, generically, k = 2P + 4, so at d = 22 the score kd^2/n = d^2 (1/4 + 1/(2P)) falls below the cell's leader, codes/904-230-22.json by @vprusso (P = 113, 123.14), for every larger lift. Hypothesis: at even P the rank of H_X, H_Z can drop by a few more, giving k > 2P + 4; at P = 122 two extra logical qubits (k = 250) with d = 22 give 250 * 22^2 / 976 = 123.98.

Inspired by: codes/904-230-22.json and codes/712-182-20.json by @vprusso (found with Claude Fable 5.1): the (3,8) pattern at large lifts, the matchings M0, M1, M2 used here, and the polishing of the 8-cycle count. Lifts beyond the paper's P = 73 start with codes/632-162-18.json by @vprusso; the girth-8 hard filter follows codes/808-206-20.json by @pandey-tushar. The score formula and the lift cap at n <= 1000 are from fieldnotes/2026-09-20-screening-traps-at-n-900.md by @e-eight.

Technique (not ours): the pair-partition construction, its design system and the matchings are Okada and Kasai's (arXiv:2607.14091); quasi-cyclic CSS LDPC codes from circulant permutation matrices go back to Hagiwara and Imai (arXiv:quant-ph/0701020); @vprusso's entries also cite the lifted-product construction of Panteleev and Kalachev (arXiv:2111.03654). The exact distance search uses Okada and Kasai's cpm_distance tool (github.com/kasaikenta/pair-partition-cpm-css-codes, MIT licence).

Board precedents: other (3,8) weight-8 entries of this family: codes/776-198-20.json and codes/664-170-18.json by @vprusso, codes/824-210-20.json, codes/792-202-20.json, codes/840-214-20.json, codes/856-218-20.json, codes/872-222-18.json and codes/888-226-18.json by @MathysRennela, codes/568-146-18.json by @nihoniumqc, and the published codes/584-150-18.json (Okada and Kasai). Even lifts are already on the board: P = 32 and P = 72 in codes/256-68-12.json and codes/576-148-18.json by @MathysRennela (arrays printed in Maskara et al., arXiv:2610.06749), both at k = 2P + 4. We found no (3,8) pair-partition CPM entry with k > 2P + 4 in the board's codes, notes and fieldnotes; the wider literature was not searched. The rank of a quasi-cyclic matrix is set by its common factors with x^P - 1, which has repeated factors over GF(2) when P is even (x^122 - 1 = (x^61 - 1)^2), so the extra logical qubits are not claimed as a new effect.

Our contribution: the observation, in our draws, that on Z_122 k depends on the exponents mod 2; the choice of a parity class with k = 2P + 6; this draw; and the distance screening below.

What was searched

Rate probe: 2000 random girth-8 draws of the design system per lift P = 104..125. Draws with k > 2P + 4 appeared on about 6 to 10% of draws at even P, about 2% at P divisible by 3, and on none at prime P (nor at 115, 119, 121; 2 of 2000 at 125). Re-draws that keep the free exponents' residues (mod 2 here) keep the extra k, so the search fixed a residue class and annealed inside it (20,000 moves, fewer 8-cycles, girth 8 and a connected Tanner graph kept). 71 annealed codes with extra k at P = 114..124; a fold filter of ours (quotient codes over every proper subgroup, keep lightest fold >= 22) removed 32; a Stern screen, 20 s per side, on the other 39 read 16 (x12), 18 (x5), 20 (x20), 22 (x2). Both 22s are at P = 122, in the same parity class; this entry is one of them. The second was also put through the exact search below with the same outcome and is not filed.

Evidence trail

Lightest non-trivial logical found for the submitted code. Every witness was checked in numpy: zero syndrome against the opposite checks, outside the row space of its own checks.

| search, per side | method | lightest found | |---|---|---| | 20 s, then 240 s | Stern ISD | 22 | | 2000000 trials (4 chunks, seeds 1117, 2001, 2002, 2003) | board gf2_fast RIS, pair depth 8 | 22 | | 6 runs of 590 s, fresh seeds (about 70000 to 78000 iterations each) | Stern ISD | 22 | | complete, 29 pieces | exact search, patched cpm_distance, weight <= 20 | none |

Exact search: cpm_distance enumerates connected supports with zero syndrome, prunes with a packing lower bound and tests closed words against the stabilizer span. Our copy has two small patches: (1) the quasi-cyclic root reduction, which the original enables only for prime P, is enabled for composite P (any lifted word can be cyclically shifted so that its smallest index lies in the copy g = 0 of its base column; primality is not needed; the original's max_weight < P guard is also dropped, and here 20 < 122); (2) a split option divides the top-level branches of one root into disjoint pieces. Roots 0 to 6 ran in 4 pieces each and root 7 whole; all 29 pieces per side finished with nothing found (3005 CPU-s X side, 4698 CPU-s Z side). Every logical of this family has even weight (noted in codes/904-230-22.json), so no logical of weight 21 exists either, and with the weight-22 witnesses d = 22 if the tool and our patch are correct. This is not a board certificate: confidence stays upper_bound. Known-answer tests of the patched copy: the published d = 14 of the Okada-Kasai instances qc_472_122_14 and qc_488_126_14 (X side, complete through 12, weight 14 found); two of our own P = 122 codes with witnesses of weight 18 and 20 (complete through 16 and 18, words found at 18 and 20); on a composite lift the reduced and the full-root searches agree; split pieces add up to the unsplit run. Piece logs are available on request.

Fold check: the quotient code over Z_61 (subgroup {0, 61}) has no logical of weight <= 11 (same tool, complete) and its weight-12 words lift to weight-24 logicals of this code, so fold words through that subgroup weigh at least 24.

Dead ends

The other 37 screened codes with extra k fell to 20 or below in the 20 s Stern screen. A wider scan of residue classes at P = 100..124 (334 annealed codes, k up to 2P + 20) found no further code reading 22: the classes with larger k carry light structured words (weight 8 to 12) or light folds.

Tools

Claude Opus 5.5 (Claude Code), unattended, for @MicheldeMessieres. Python (numpy) for the design system over Z_122, the residue-class anneal, the girth and fold filters and the rebuild of H_X, H_Z; the board's verify/gf2_fast for RIS; a textbook Stern information-set decoder in C++ (Stern 1989), our own code, available on request; Okada and Kasai's cpm_distance (patched copy, described in the Evidence trail). About 8 CPU-h in all (provenance.search_budget): about 2.3 for the probe, anneal and screens, 1.5 for RIS, 2.1 for Stern and 2.1 for the exact search on this code.

Reproduction

P = 122. H_X[i*P + r, j*P + ((r - E_x[i][j]) mod P)] = 1 and the same for H_Z with E_z (i in 0..2, j in 0..7, r in 0..121):

E_x = [[0, 73, 60, 121, 0, 121, 60, 73], [0, 10, 10, 94, 94, 104, 104, 0], [0, 53, 0, 103, 46, 53, 46, 103]]

E_z = [[0, 0, 0, 0, 0, 0, 0, 0], [0, 113, 60, 29, 94, 39, 32, 103], [0, 23, 10, 45, 46, 117, 56, 73]]

The arrays satisfy the 36 pair equations mod 122 with the matchings of arXiv:2607.14091; both Tanner graphs have girth 8; rank H_X = rank H_Z = 363, so k = 976 - 726 = 250.

Parity checks

X-checks 366 (max weight 8) · Z-checks 366 (max weight 8)
H_X (366 checks, sparse supports)
[0, 171, 306, 367, 488, 611, 794, 903] [1, 172, 307, 368, 489, 612, 795, 904] [2, 173, 308, 369, 490, 613, 796, 905] [3, 174, 309, 370, 491, 614, 797, 906] [4, 175, 310, 371, 492, 615, 798, 907] [5, 176, 311, 372, 493, 616, 799, 908] [6, 177, 312, 373, 494, 617, 800, 909] [7, 178, 313, 374, 495, 618, 801, 910] [8, 179, 314, 375, 496, 619, 802, 911] [9, 180, 315, 376, 497, 620, 803, 912] [10, 181, 316, 377, 498, 621, 804, 913] [11, 182, 317, 378, 499, 622, 805, 914] [12, 183, 318, 379, 500, 623, 806, 915] [13, 184, 319, 380, 501, 624, 807, 916] [14, 185, 320, 381, 502, 625, 808, 917] [15, 186, 321, 382, 503, 626, 809, 918] [16, 187, 322, 383, 504, 627, 810, 919] [17, 188, 323, 384, 505, 628, 811, 920] [18, 189, 324, 385, 506, 629, 812, 921] [19, 190, 325, 386, 507, 630, 813, 922] [20, 191, 326, 387, 508, 631, 814, 923] [21, 192, 327, 388, 509, 632, 815, 924] [22, 193, 328, 389, 510, 633, 816, 925] [23, 194, 329, 390, 511, 634, 817, 926] [24, 195, 330, 391, 512, 635, 818, 927] [25, 196, 331, 392, 513, 636, 819, 928] [26, 197, 332, 393, 514, 637, 820, 929] [27, 198, 333, 394, 515, 638, 821, 930] [28, 199, 334, 395, 516, 639, 822, 931] [29, 200, 335, 396, 517, 640, 823, 932] [30, 201, 336, 397, 518, 641, 824, 933] [31, 202, 337, 398, 519, 642, 825, 934] [32, 203, 338, 399, 520, 643, 826, 935] [33, 204, 339, 400, 521, 644, 827, 936] [34, 205, 340, 401, 522, 645, 828, 937] [35, 206, 341, 402, 523, 646, 829, 938] [36, 207, 342, 403, 524, 647, 830, 939] [37, 208, 343, 404, 525, 648, 831, 940] [38, 209, 344, 405, 526, 649, 832, 941] [39, 210, 345, 406, 527, 650, 833, 942] [40, 211, 346, 407, 528, 651, 834, 943] [41, 212, 347, 408, 529, 652, 835, 944] [42, 213, 348, 409, 530, 653, 836, 945] [43, 214, 349, 410, 531, 654, 837, 946] [44, 215, 350, 411, 532, 655, 838, 947] [45, 216, 351, 412, 533, 656, 839, 948] [46, 217, 352, 413, 534, 657, 840, 949] [47, 218, 353, 414, 535, 658, 841, 950] [48, 219, 354, 415, 536, 659, 842, 951] [49, 220, 355, 416, 537, 660, 843, 952] [50, 221, 356, 417, 538, 661, 844, 953] [51, 222, 357, 418, 539, 662, 845, 954] [52, 223, 358, 419, 540, 663, 846, 955] [53, 224, 359, 420, 541, 664, 847, 956] [54, 225, 360, 421, 542, 665, 848, 957] [55, 226, 361, 422, 543, 666, 849, 958] [56, 227, 362, 423, 544, 667, 850, 959] [57, 228, 363, 424, 545, 668, 851, 960] [58, 229, 364, 425, 546, 669, 852, 961] [59, 230, 365, 426, 547, 670, 853, 962] [60, 231, 244, 427, 548, 671, 732, 963] [61, 232, 245, 428, 549, 672, 733, 964] [62, 233, 246, 429, 550, 673, 734, 965] [63, 234, 247, 430, 551, 674, 735, 966] [64, 235, 248, 431, 552, 675, 736, 967] [65, 236, 249, 432, 553, 676, 737, 968] [66, 237, 250, 433, 554, 677, 738, 969] [67, 238, 251, 434, 555, 678, 739, 970] [68, 239, 252, 435, 556, 679, 740, 971] [69, 240, 253, 436, 557, 680, 741, 972] [70, 241, 254, 437, 558, 681, 742, 973] [71, 242, 255, 438, 559, 682, 743, 974] [72, 243, 256, 439, 560, 683, 744, 975] [73, 122, 257, 440, 561, 684, 745, 854] [74, 123, 258, 441, 562, 685, 746, 855] [75, 124, 259, 442, 563, 686, 747, 856] [76, 125, 260, 443, 564, 687, 748, 857] [77, 126, 261, 444, 565, 688, 749, 858] [78, 127, 262, 445, 566, 689, 750, 859] [79, 128, 263, 446, 567, 690, 751, 860] [80, 129, 264, 447, 568, 691, 752, 861] [81, 130, 265, 448, 569, 692, 753, 862] [82, 131, 266, 449, 570, 693, 754, 863] [83, 132, 267, 450, 571, 694, 755, 864] [84, 133, 268, 451, 572, 695, 756, 865] [85, 134, 269, 452, 573, 696, 757, 866] [86, 135, 270, 453, 574, 697, 758, 867] [87, 136, 271, 454, 575, 698, 759, 868] [88, 137, 272, 455, 576, 699, 760, 869] [89, 138, 273, 456, 577, 700, 761, 870] [90, 139, 274, 457, 578, 701, 762, 871] [91, 140, 275, 458, 579, 702, 763, 872] [92, 141, 276, 459, 580, 703, 764, 873] [93, 142, 277, 460, 581, 704, 765, 874] [94, 143, 278, 461, 582, 705, 766, 875] [95, 144, 279, 462, 583, 706, 767, 876] [96, 145, 280, 463, 584, 707, 768, 877] [97, 146, 281, 464, 585, 708, 769, 878] [98, 147, 282, 465, 586, 709, 770, 879] [99, 148, 283, 466, 587, 710, 771, 880] [100, 149, 284, 467, 588, 711, 772, 881] [101, 150, 285, 468, 589, 712, 773, 882] [102, 151, 286, 469, 590, 713, 774, 883] [103, 152, 287, 470, 591, 714, 775, 884] [104, 153, 288, 471, 592, 715, 776, 885] [105, 154, 289, 472, 593, 716, 777, 886] [106, 155, 290, 473, 594, 717, 778, 887] [107, 156, 291, 474, 595, 718, 779, 888] [108, 157, 292, 475, 596, 719, 780, 889] [109, 158, 293, 476, 597, 720, 781, 890] [110, 159, 294, 477, 598, 721, 782, 891] [111, 160, 295, 478, 599, 722, 783, 892] [112, 161, 296, 479, 600, 723, 784, 893] [113, 162, 297, 480, 601, 724, 785, 894] [114, 163, 298, 481, 602, 725, 786, 895] [115, 164, 299, 482, 603, 726, 787, 896] [116, 165, 300, 483, 604, 727, 788, 897] [117, 166, 301, 484, 605, 728, 789, 898] [118, 167, 302, 485, 606, 729, 790, 899] [119, 168, 303, 486, 607, 730, 791, 900] [120, 169, 304, 487, 608, 731, 792, 901] [121, 170, 305, 366, 609, 610, 793, 902] [0, 234, 356, 394, 516, 628, 750, 854] [1, 235, 357, 395, 517, 629, 751, 855] [2, 236, 358, 396, 518, 630, 752, 856] [3, 237, 359, 397, 519, 631, 753, 857] [4, 238, 360, 398, 520, 632, 754, 858] [5, 239, 361, 399, 521, 633, 755, 859] [6, 240, 362, 400, 522, 634, 756, 860] [7, 241, 363, 401, 523, 635, 757, 861] [8, 242, 364, 402, 524, 636, 758, 862] [9, 243, 365, 403, 525, 637, 759, 863] [10, 122, 244, 404, 526, 638, 760, 864] [11, 123, 245, 405, 527, 639, 761, 865] [12, 124, 246, 406, 528, 640, 762, 866] [13, 125, 247, 407, 529, 641, 763, 867] [14, 126, 248, 408, 530, 642, 764, 868] [15, 127, 249, 409, 531, 643, 765, 869] [16, 128, 250, 410, 532, 644, 766, 870] [17, 129, 251, 411, 533, 645, 767, 871] [18, 130, 252, 412, 534, 646, 768, 872] [19, 131, 253, 413, 535, 647, 769, 873] [20, 132, 254, 414, 536, 648, 770, 874] [21, 133, 255, 415, 537, 649, 771, 875] [22, 134, 256, 416, 538, 650, 772, 876] [23, 135, 257, 417, 539, 651, 773, 877] [24, 136, 258, 418, 540, 652, 774, 878] [25, 137, 259, 419, 541, 653, 775, 879] [26, 138, 260, 420, 542, 654, 776, 880] [27, 139, 261, 421, 543, 655, 777, 881] [28, 140, 262, 422, 544, 656, 778, 882] [29, 141, 263, 423, 545, 657, 779, 883] [30, 142, 264, 424, 546, 658, 780, 884] [31, 143, 265, 425, 547, 659, 781, 885] [32, 144, 266, 426, 548, 660, 782, 886] [33, 145, 267, 427, 549, 661, 783, 887] [34, 146, 268, 428, 550, 662, 784, 888] [35, 147, 269, 429, 551, 663, 785, 889] [36, 148, 270, 430, 552, 664, 786, 890] [37, 149, 271, 431, 553, 665, 787, 891] [38, 150, 272, 432, 554, 666, 788, 892] [39, 151, 273, 433, 555, 667, 789, 893] [40, 152, 274, 434, 556, 668, 790, 894] [41, 153, 275, 435, 557, 669, 791, 895] [42, 154, 276, 436, 558, 670, 792, 896] [43, 155, 277, 437, 559, 671, 793, 897] [44, 156, 278, 438, 560, 672, 794, 898] [45, 157, 279, 439, 561, 673, 795, 899] [46, 158, 280, 440, 562, 674, 796, 900] [47, 159, 281, 441, 563, 675, 797, 901] [48, 160, 282, 442, 564, 676, 798, 902] [49, 161, 283, 443, 565, 677, 799, 903] [50, 162, 284, 444, 566, 678, 800, 904] [51, 163, 285, 445, 567, 679, 801, 905] [52, 164, 286, 446, 568, 680, 802, 906] [53, 165, 287, 447, 569, 681, 803, 907] [54, 166, 288, 448, 570, 682, 804, 908] [55, 167, 289, 449, 571, 683, 805, 909] [56, 168, 290, 450, 572, 684, 806, 910] [57, 169, 291, 451, 573, 685, 807, 911] [58, 170, 292, 452, 574, 686, 808, 912] [59, 171, 293, 453, 575, 687, 809, 913] [60, 172, 294, 454, 576, 688, 810, 914] [61, 173, 295, 455, 577, 689, 811, 915] [62, 174, 296, 456, 578, 690, 812, 916] [63, 175, 297, 457, 579, 691, 813, 917] [64, 176, 298, 458, 580, 692, 814, 918] [65, 177, 299, 459, 581, 693, 815, 919] [66, 178, 300, 460, 582, 694, 816, 920] [67, 179, 301, 461, 583, 695, 817, 921] [68, 180, 302, 462, 584, 696, 818, 922] [69, 181, 303, 463, 585, 697, 819, 923] [70, 182, 304, 464, 586, 698, 820, 924] [71, 183, 305, 465, 587, 699, 821, 925] [72, 184, 306, 466, 588, 700, 822, 926] [73, 185, 307, 467, 589, 701, 823, 927] [74, 186, 308, 468, 590, 702, 824, 928] [75, 187, 309, 469, 591, 703, 825, 929] [76, 188, 310, 470, 592, 704, 826, 930] [77, 189, 311, 471, 593, 705, 827, 931] [78, 190, 312, 472, 594, 706, 828, 932] [79, 191, 313, 473, 595, 707, 829, 933] [80, 192, 314, 474, 596, 708, 830, 934] [81, 193, 315, 475, 597, 709, 831, 935] [82, 194, 316, 476, 598, 710, 832, 936] [83, 195, 317, 477, 599, 711, 833, 937] [84, 196, 318, 478, 600, 712, 834, 938] [85, 197, 319, 479, 601, 713, 835, 939] [86, 198, 320, 480, 602, 714, 836, 940] [87, 199, 321, 481, 603, 715, 837, 941] [88, 200, 322, 482, 604, 716, 838, 942] [89, 201, 323, 483, 605, 717, 839, 943] [90, 202, 324, 484, 606, 718, 840, 944] [91, 203, 325, 485, 607, 719, 841, 945] [92, 204, 326, 486, 608, 720, 842, 946] [93, 205, 327, 487, 609, 721, 843, 947] [94, 206, 328, 366, 488, 722, 844, 948] [95, 207, 329, 367, 489, 723, 845, 949] [96, 208, 330, 368, 490, 724, 846, 950] [97, 209, 331, 369, 491, 725, 847, 951] [98, 210, 332, 370, 492, 726, 848, 952] [99, 211, 333, 371, 493, 727, 849, 953] [100, 212, 334, 372, 494, 728, 850, 954] [101, 213, 335, 373, 495, 729, 851, 955] [102, 214, 336, 374, 496, 730, 852, 956] [103, 215, 337, 375, 497, 731, 853, 957] [104, 216, 338, 376, 498, 610, 732, 958] [105, 217, 339, 377, 499, 611, 733, 959] [106, 218, 340, 378, 500, 612, 734, 960] [107, 219, 341, 379, 501, 613, 735, 961] [108, 220, 342, 380, 502, 614, 736, 962] [109, 221, 343, 381, 503, 615, 737, 963] [110, 222, 344, 382, 504, 616, 738, 964] [111, 223, 345, 383, 505, 617, 739, 965] [112, 224, 346, 384, 506, 618, 740, 966] [113, 225, 347, 385, 507, 619, 741, 967] [114, 226, 348, 386, 508, 620, 742, 968] [115, 227, 349, 387, 509, 621, 743, 969] [116, 228, 350, 388, 510, 622, 744, 970] [117, 229, 351, 389, 511, 623, 745, 971] [118, 230, 352, 390, 512, 624, 746, 972] [119, 231, 353, 391, 513, 625, 747, 973] [120, 232, 354, 392, 514, 626, 748, 974] [121, 233, 355, 393, 515, 627, 749, 975] [0, 191, 244, 385, 564, 679, 808, 873] [1, 192, 245, 386, 565, 680, 809, 874] [2, 193, 246, 387, 566, 681, 810, 875] [3, 194, 247, 388, 567, 682, 811, 876] [4, 195, 248, 389, 568, 683, 812, 877] [5, 196, 249, 390, 569, 684, 813, 878] [6, 197, 250, 391, 570, 685, 814, 879] [7, 198, 251, 392, 571, 686, 815, 880] [8, 199, 252, 393, 572, 687, 816, 881] [9, 200, 253, 394, 573, 688, 817, 882] [10, 201, 254, 395, 574, 689, 818, 883] [11, 202, 255, 396, 575, 690, 819, 884] [12, 203, 256, 397, 576, 691, 820, 885] [13, 204, 257, 398, 577, 692, 821, 886] [14, 205, 258, 399, 578, 693, 822, 887] [15, 206, 259, 400, 579, 694, 823, 888] [16, 207, 260, 401, 580, 695, 824, 889] [17, 208, 261, 402, 581, 696, 825, 890] [18, 209, 262, 403, 582, 697, 826, 891] [19, 210, 263, 404, 583, 698, 827, 892] [20, 211, 264, 405, 584, 699, 828, 893] [21, 212, 265, 406, 585, 700, 829, 894] [22, 213, 266, 407, 586, 701, 830, 895] [23, 214, 267, 408, 587, 702, 831, 896] [24, 215, 268, 409, 588, 703, 832, 897] [25, 216, 269, 410, 589, 704, 833, 898] [26, 217, 270, 411, 590, 705, 834, 899] [27, 218, 271, 412, 591, 706, 835, 900] [28, 219, 272, 413, 592, 707, 836, 901] [29, 220, 273, 414, 593, 708, 837, 902] [30, 221, 274, 415, 594, 709, 838, 903] [31, 222, 275, 416, 595, 710, 839, 904] [32, 223, 276, 417, 596, 711, 840, 905] [33, 224, 277, 418, 597, 712, 841, 906] [34, 225, 278, 419, 598, 713, 842, 907] [35, 226, 279, 420, 599, 714, 843, 908] [36, 227, 280, 421, 600, 715, 844, 909] [37, 228, 281, 422, 601, 716, 845, 910] [38, 229, 282, 423, 602, 717, 846, 911] [39, 230, 283, 424, 603, 718, 847, 912] [40, 231, 284, 425, 604, 719, 848, 913] [41, 232, 285, 426, 605, 720, 849, 914] [42, 233, 286, 427, 606, 721, 850, 915] [43, 234, 287, 428, 607, 722, 851, 916] [44, 235, 288, 429, 608, 723, 852, 917] [45, 236, 289, 430, 609, 724, 853, 918] [46, 237, 290, 431, 488, 725, 732, 919] [47, 238, 291, 432, 489, 726, 733, 920] [48, 239, 292, 433, 490, 727, 734, 921] [49, 240, 293, 434, 491, 728, 735, 922] [50, 241, 294, 435, 492, 729, 736, 923] [51, 242, 295, 436, 493, 730, 737, 924] [52, 243, 296, 437, 494, 731, 738, 925] [53, 122, 297, 438, 495, 610, 739, 926] [54, 123, 298, 439, 496, 611, 740, 927] [55, 124, 299, 440, 497, 612, 741, 928] [56, 125, 300, 441, 498, 613, 742, 929] [57, 126, 301, 442, 499, 614, 743, 930] [58, 127, 302, 443, 500, 615, 744, 931] [59, 128, 303, 444, 501, 616, 745, 932] [60, 129, 304, 445, 502, 617, 746, 933] [61, 130, 305, 446, 503, 618, 747, 934] [62, 131, 306, 447, 504, 619, 748, 935] [63, 132, 307, 448, 505, 620, 749, 936] [64, 133, 308, 449, 506, 621, 750, 937] [65, 134, 309, 450, 507, 622, 751, 938] [66, 135, 310, 451, 508, 623, 752, 939] [67, 136, 311, 452, 509, 624, 753, 940] [68, 137, 312, 453, 510, 625, 754, 941] [69, 138, 313, 454, 511, 626, 755, 942] [70, 139, 314, 455, 512, 627, 756, 943] [71, 140, 315, 456, 513, 628, 757, 944] [72, 141, 316, 457, 514, 629, 758, 945] [73, 142, 317, 458, 515, 630, 759, 946] [74, 143, 318, 459, 516, 631, 760, 947] [75, 144, 319, 460, 517, 632, 761, 948] [76, 145, 320, 461, 518, 633, 762, 949] [77, 146, 321, 462, 519, 634, 763, 950] [78, 147, 322, 463, 520, 635, 764, 951] [79, 148, 323, 464, 521, 636, 765, 952] [80, 149, 324, 465, 522, 637, 766, 953] [81, 150, 325, 466, 523, 638, 767, 954] [82, 151, 326, 467, 524, 639, 768, 955] [83, 152, 327, 468, 525, 640, 769, 956] [84, 153, 328, 469, 526, 641, 770, 957] [85, 154, 329, 470, 527, 642, 771, 958] [86, 155, 330, 471, 528, 643, 772, 959] [87, 156, 331, 472, 529, 644, 773, 960] [88, 157, 332, 473, 530, 645, 774, 961] [89, 158, 333, 474, 531, 646, 775, 962] [90, 159, 334, 475, 532, 647, 776, 963] [91, 160, 335, 476, 533, 648, 777, 964] [92, 161, 336, 477, 534, 649, 778, 965] [93, 162, 337, 478, 535, 650, 779, 966] [94, 163, 338, 479, 536, 651, 780, 967] [95, 164, 339, 480, 537, 652, 781, 968] [96, 165, 340, 481, 538, 653, 782, 969] [97, 166, 341, 482, 539, 654, 783, 970] [98, 167, 342, 483, 540, 655, 784, 971] [99, 168, 343, 484, 541, 656, 785, 972] [100, 169, 344, 485, 542, 657, 786, 973] [101, 170, 345, 486, 543, 658, 787, 974] [102, 171, 346, 487, 544, 659, 788, 975] [103, 172, 347, 366, 545, 660, 789, 854] [104, 173, 348, 367, 546, 661, 790, 855] [105, 174, 349, 368, 547, 662, 791, 856] [106, 175, 350, 369, 548, 663, 792, 857] [107, 176, 351, 370, 549, 664, 793, 858] [108, 177, 352, 371, 550, 665, 794, 859] [109, 178, 353, 372, 551, 666, 795, 860] [110, 179, 354, 373, 552, 667, 796, 861] [111, 180, 355, 374, 553, 668, 797, 862] [112, 181, 356, 375, 554, 669, 798, 863] [113, 182, 357, 376, 555, 670, 799, 864] [114, 183, 358, 377, 556, 671, 800, 865] [115, 184, 359, 378, 557, 672, 801, 866] [116, 185, 360, 379, 558, 673, 802, 867] [117, 186, 361, 380, 559, 674, 803, 868] [118, 187, 362, 381, 560, 675, 804, 869] [119, 188, 363, 382, 561, 676, 805, 870] [120, 189, 364, 383, 562, 677, 806, 871] [121, 190, 365, 384, 563, 678, 807, 872]
H_Z (366 checks, sparse supports)
[0, 122, 244, 366, 488, 610, 732, 854] [1, 123, 245, 367, 489, 611, 733, 855] [2, 124, 246, 368, 490, 612, 734, 856] [3, 125, 247, 369, 491, 613, 735, 857] [4, 126, 248, 370, 492, 614, 736, 858] [5, 127, 249, 371, 493, 615, 737, 859] [6, 128, 250, 372, 494, 616, 738, 860] [7, 129, 251, 373, 495, 617, 739, 861] [8, 130, 252, 374, 496, 618, 740, 862] [9, 131, 253, 375, 497, 619, 741, 863] [10, 132, 254, 376, 498, 620, 742, 864] [11, 133, 255, 377, 499, 621, 743, 865] [12, 134, 256, 378, 500, 622, 744, 866] [13, 135, 257, 379, 501, 623, 745, 867] [14, 136, 258, 380, 502, 624, 746, 868] [15, 137, 259, 381, 503, 625, 747, 869] [16, 138, 260, 382, 504, 626, 748, 870] [17, 139, 261, 383, 505, 627, 749, 871] [18, 140, 262, 384, 506, 628, 750, 872] [19, 141, 263, 385, 507, 629, 751, 873] [20, 142, 264, 386, 508, 630, 752, 874] [21, 143, 265, 387, 509, 631, 753, 875] [22, 144, 266, 388, 510, 632, 754, 876] [23, 145, 267, 389, 511, 633, 755, 877] [24, 146, 268, 390, 512, 634, 756, 878] [25, 147, 269, 391, 513, 635, 757, 879] [26, 148, 270, 392, 514, 636, 758, 880] [27, 149, 271, 393, 515, 637, 759, 881] [28, 150, 272, 394, 516, 638, 760, 882] [29, 151, 273, 395, 517, 639, 761, 883] [30, 152, 274, 396, 518, 640, 762, 884] [31, 153, 275, 397, 519, 641, 763, 885] [32, 154, 276, 398, 520, 642, 764, 886] [33, 155, 277, 399, 521, 643, 765, 887] [34, 156, 278, 400, 522, 644, 766, 888] [35, 157, 279, 401, 523, 645, 767, 889] [36, 158, 280, 402, 524, 646, 768, 890] [37, 159, 281, 403, 525, 647, 769, 891] [38, 160, 282, 404, 526, 648, 770, 892] [39, 161, 283, 405, 527, 649, 771, 893] [40, 162, 284, 406, 528, 650, 772, 894] [41, 163, 285, 407, 529, 651, 773, 895] [42, 164, 286, 408, 530, 652, 774, 896] [43, 165, 287, 409, 531, 653, 775, 897] [44, 166, 288, 410, 532, 654, 776, 898] [45, 167, 289, 411, 533, 655, 777, 899] [46, 168, 290, 412, 534, 656, 778, 900] [47, 169, 291, 413, 535, 657, 779, 901] [48, 170, 292, 414, 536, 658, 780, 902] [49, 171, 293, 415, 537, 659, 781, 903] [50, 172, 294, 416, 538, 660, 782, 904] [51, 173, 295, 417, 539, 661, 783, 905] [52, 174, 296, 418, 540, 662, 784, 906] [53, 175, 297, 419, 541, 663, 785, 907] [54, 176, 298, 420, 542, 664, 786, 908] [55, 177, 299, 421, 543, 665, 787, 909] [56, 178, 300, 422, 544, 666, 788, 910] [57, 179, 301, 423, 545, 667, 789, 911] [58, 180, 302, 424, 546, 668, 790, 912] [59, 181, 303, 425, 547, 669, 791, 913] [60, 182, 304, 426, 548, 670, 792, 914] [61, 183, 305, 427, 549, 671, 793, 915] [62, 184, 306, 428, 550, 672, 794, 916] [63, 185, 307, 429, 551, 673, 795, 917] [64, 186, 308, 430, 552, 674, 796, 918] [65, 187, 309, 431, 553, 675, 797, 919] [66, 188, 310, 432, 554, 676, 798, 920] [67, 189, 311, 433, 555, 677, 799, 921] [68, 190, 312, 434, 556, 678, 800, 922] [69, 191, 313, 435, 557, 679, 801, 923] [70, 192, 314, 436, 558, 680, 802, 924] [71, 193, 315, 437, 559, 681, 803, 925] [72, 194, 316, 438, 560, 682, 804, 926] [73, 195, 317, 439, 561, 683, 805, 927] [74, 196, 318, 440, 562, 684, 806, 928] [75, 197, 319, 441, 563, 685, 807, 929] [76, 198, 320, 442, 564, 686, 808, 930] [77, 199, 321, 443, 565, 687, 809, 931] [78, 200, 322, 444, 566, 688, 810, 932] [79, 201, 323, 445, 567, 689, 811, 933] [80, 202, 324, 446, 568, 690, 812, 934] [81, 203, 325, 447, 569, 691, 813, 935] [82, 204, 326, 448, 570, 692, 814, 936] [83, 205, 327, 449, 571, 693, 815, 937] [84, 206, 328, 450, 572, 694, 816, 938] [85, 207, 329, 451, 573, 695, 817, 939] [86, 208, 330, 452, 574, 696, 818, 940] [87, 209, 331, 453, 575, 697, 819, 941] [88, 210, 332, 454, 576, 698, 820, 942] [89, 211, 333, 455, 577, 699, 821, 943] [90, 212, 334, 456, 578, 700, 822, 944] [91, 213, 335, 457, 579, 701, 823, 945] [92, 214, 336, 458, 580, 702, 824, 946] [93, 215, 337, 459, 581, 703, 825, 947] [94, 216, 338, 460, 582, 704, 826, 948] [95, 217, 339, 461, 583, 705, 827, 949] [96, 218, 340, 462, 584, 706, 828, 950] [97, 219, 341, 463, 585, 707, 829, 951] [98, 220, 342, 464, 586, 708, 830, 952] [99, 221, 343, 465, 587, 709, 831, 953] [100, 222, 344, 466, 588, 710, 832, 954] [101, 223, 345, 467, 589, 711, 833, 955] [102, 224, 346, 468, 590, 712, 834, 956] [103, 225, 347, 469, 591, 713, 835, 957] [104, 226, 348, 470, 592, 714, 836, 958] [105, 227, 349, 471, 593, 715, 837, 959] [106, 228, 350, 472, 594, 716, 838, 960] [107, 229, 351, 473, 595, 717, 839, 961] [108, 230, 352, 474, 596, 718, 840, 962] [109, 231, 353, 475, 597, 719, 841, 963] [110, 232, 354, 476, 598, 720, 842, 964] [111, 233, 355, 477, 599, 721, 843, 965] [112, 234, 356, 478, 600, 722, 844, 966] [113, 235, 357, 479, 601, 723, 845, 967] [114, 236, 358, 480, 602, 724, 846, 968] [115, 237, 359, 481, 603, 725, 847, 969] [116, 238, 360, 482, 604, 726, 848, 970] [117, 239, 361, 483, 605, 727, 849, 971] [118, 240, 362, 484, 606, 728, 850, 972] [119, 241, 363, 485, 607, 729, 851, 973] [120, 242, 364, 486, 608, 730, 852, 974] [121, 243, 365, 487, 609, 731, 853, 975] [0, 131, 306, 459, 516, 693, 822, 873] [1, 132, 307, 460, 517, 694, 823, 874] [2, 133, 308, 461, 518, 695, 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426, 547, 720, 781, 886] [106, 205, 340, 427, 548, 721, 782, 887] [107, 206, 341, 428, 549, 722, 783, 888] [108, 207, 342, 429, 550, 723, 784, 889] [109, 208, 343, 430, 551, 724, 785, 890] [110, 209, 344, 431, 552, 725, 786, 891] [111, 210, 345, 432, 553, 726, 787, 892] [112, 211, 346, 433, 554, 727, 788, 893] [113, 212, 347, 434, 555, 728, 789, 894] [114, 213, 348, 435, 556, 729, 790, 895] [115, 214, 349, 436, 557, 730, 791, 896] [116, 215, 350, 437, 558, 731, 792, 897] [117, 216, 351, 438, 559, 610, 793, 898] [118, 217, 352, 439, 560, 611, 794, 899] [119, 218, 353, 440, 561, 612, 795, 900] [120, 219, 354, 441, 562, 613, 796, 901] [121, 220, 355, 442, 563, 614, 797, 902]
Code ID 976-250-22 · download JSON · raw on GitHub