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[[994,142,40]] d ≤
n
994
k
142
d
40
kd²/n
228.571
w
8
X/Z
1.02

Share this result

Distance

X/Z asymmetry 1.02 · d_X ≤ 41, d_Z ≤ 40 · 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 41 · witness weight 41 (claimed upper_bound)
witness operator (support, 41 qubits)
[14, 181, 185, 212, 241, 269, 305, 310, 324, 336, 403, 440, 452, 454, 466, 493, 495, 522, 579, 602, 613, 617, 625, 661, 667, 712, 739, 761, 802, 804, 815, 841, 870, 926, 929, 931, 933, 941, 961, 974, 975]
d_Z 40 · witness weight 40 (claimed upper_bound)
witness found by @MicheldeMessieres · isd_fast (Stern, p 2, window 16) · found at 4.6×104 trials · 2026-10-28
witness operator (support, 40 qubits)
[8, 16, 27, 32, 133, 136, 238, 257, 286, 338, 343, 373, 392, 410, 427, 432, 440, 476, 490, 506, 560, 563, 576, 696, 712, 728, 740, 764, 778, 783, 799, 812, 835, 845, 877, 888, 896, 907, 950, 964]
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 8 · H_Z 8
qubit degrees H_X 3–4 (mean 3.429) · H_Z 3–4 (mean 3.429)
trapping sets H_X (1,3)×568 (2,4)×3124 (3,4)×142 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 568 (1,4): 426 (2,4): 3124 (2,5): 5680 (2,6): 3124 (3,4): 142 (3,5): 22578 (3,6): 70574 (3,7): 86194 (3,8): 37772 (3,9): 8520 (3,10): 3408
trapping sets H_Z (1,3)×568 (2,4)×3124 (3,4)×142 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 568 (1,4): 426 (2,4): 3124 (2,5): 5680 (2,6): 3124 (3,4): 142 (3,5): 22578 (3,6): 70574 (3,7): 86194 (3,8): 37772 (3,9): 8520 (3,10): 3408

Construction & provenance

provenance submitted through the challenge
novelty novelty not audited
construction Pair-partition CPM CSS code: the pair-partition commutation rule of Okada-Kasai (arXiv:2607.14091) on a 6x14 'pair-closed' base template, cyclic lift N=71 (Z_71), n=14N=994, design rate 1-(6+6)/14=1/7, k=142 (no extra dependencies). Template (the same on the X and the Z side): the 14 block columns form 7 column pairs {0,1},{2,3},...,{12,13}; each of the 6 block rows is the union of 4 of the 7 pairs, so every check has weight 8; rows by pairs: [[0, 1, 2, 5], [0, 2, 3, 5], [0, 3, 4, 6], [1, 3, 5, 6], [1, 2, 4, 6], [0, 1, 2, 4]] (pair degrees {0: 4, 1: 4, 2: 4, 3: 3, 4: 3, 5: 3, 6: 3}: qubit degree 3 or 4). Block columns per block row: [[0, 1, 2, 3, 4, 5, 10, 11], [0, 1, 4, 5, 6, 7, 10, 11], [0, 1, 6, 7, 8, 9, 12, 13], [2, 3, 6, 7, 10, 11, 12, 13], [2, 3, 4, 5, 8, 9, 12, 13], [0, 1, 2, 3, 4, 5, 8, 9]]. Every X-row/Z-row overlap is split into column pairs (the pairing below), and the exponents solve x_ia - z_ja - x_ib + z_jb = 0 (mod 71) for every column pair (a,b) in the pairing of X block row i with Z block row j, so H_X H_Z^T = 0 term by term. H[i*N + r, c*N + ((r + s_ic) mod N)] = 1 with exponents s (rows = block rows, '-' = empty cell): S_X = [[62, 40, 7, 40, 37, 52, -, -, -, -, 27, 27, -, -], [41, 0, -, -, 8, 4, 4, 20, -, -, 16, 21, -, -], [49, 32, -, -, -, -, 31, 33, 33, 16, -, -, 6, 65], [-, -, 8, 8, -, -, 0, 49, -, -, 53, 25, 5, 12], [-, -, 29, 15, 70, 0, -, -, 69, 9, -, -, 7, 38], [5, 21, 54, 59, 32, 52, -, -, 68, 13, -, -, -, -]], S_Z = [[9, 63, 25, 63, 47, 67, -, -, -, -, 37, 42, -, -], [49, 13, -, -, 24, 25, 12, 33, -, -, 37, 37, -, -], [17, 66, -, -, -, -, 70, 67, 42, 25, -, -, 23, 11], [-, -, 22, 27, -, -, 68, 46, -, -, 42, 14, 19, 31], [-, -, 32, 13, 10, 6, -, -, 4, 20, -, -, 10, 36], [64, 4, 42, 42, 12, 27, -, -, 48, 59, -, -, -, -]]. Pairing (X-row,Z-row): {"0,0":[[0,2],[1,3],[4,10],[5,11]],"0,1":[[0,4],[1,5],[10,11]],"0,2":[[0,1]],"0,3":[[2,10],[3,11]],"0,4":[[2,5],[3,4]],"0,5":[[0,3],[1,2],[4,5]],"1,0":[[0,4],[1,5],[10,11]],"1,1":[[0,6],[1,7],[4,11],[5,10]],"1,2":[[0,7],[1,6]],"1,3":[[6,11],[7,10]],"1,4":[[4,5]],"1,5":[[0,5],[1,4]],"2,0":[[0,1]],"2,1":[[0,7],[1,6]],"2,2":[[0,6],[1,7],[8,9],[12,13]],"2,3":[[6,13],[7,12]],"2,4":[[8,13],[9,12]],"2,5":[[0,8],[1,9]],"3,0":[[2,11],[3,10]],"3,1":[[6,11],[7,10]],"3,2":[[6,13],[7,12]],"3,3":[[2,12],[3,13],[6,7],[10,11]],"3,4":[[2,13],[3,12]],"3,5":[[2,3]],"4,0":[[2,5],[3,4]],"4,1":[[4,5]],"4,2":[[8,13],[9,12]],"4,3":[[2,13],[3,12]],"4,4":[[2,12],[3,13],[4,9],[5,8]],"4,5":[[2,4],[3,5],[8,9]],"5,0":[[0,3],[1,2],[4,5]],"5,1":[[0,5],[1,4]],"5,2":[[0,9],[1,8]],"5,3":[[2,3]],"5,4":[[2,4],[3,5],[8,9]],"5,5":[[0,2],[1,3],[4,8],[5,9]]}.
model Claude Claude Opus 5.5 (Claude Code) (claimed, not verified)
date 2026-10-29
notes Our contribution: the 6x14 pair-closed template (7 column pairs, every block row the union of 4 pairs, design rate 1/7), chosen because a typical-distance estimate of the LDPC ensemble with its column-degree mix (the Gallager weight-distribution estimate; Gallager, Low-Density Parity-Check Codes, MIT Press 1963) put rate 1/7 at the best ratio of predicted distance to the distance a rate-1/7 code needs; the search for its pairings (our couple solver, a search for pairings whose exponent equations keep free dimensions, run under one cyclic symmetry of the template at a time; this pairing is one of the solutions with 3 free exponent dimensions of one template class); the lift N = 71 and this exponent draw; and the distance screening. Construction framework, not ours: the pair-partition construction and its paired-difference equations on CPM exponents are Okada and Kasai's (arXiv:2607.14091); the design-rate count R = 1 - J_tot/L_stab and the permanent-vector upper bound used to rank templates (App. A of arXiv:2609.30069) are from Lee, Okada, Maskara, Kasai and Zhou (arXiv:2609.30069); quasi-cyclic CSS LDPC codes from circulant permutation matrices go back to Hagiwara and Imai (arXiv:quant-ph/0701020), and CSS pairs of two irregular LDPC codes were analysed by Hagiwara and Imai (arXiv:0801.1361). Board precedents of the same commutation rule at weight 8: codes/996-166-36.json by @jacksongquera and our codes/996-166-32.json and codes/996-166-34.json (irregular 5x12 template, rate 1/6), codes/912-234-22.json by @jacksongquera and codes/904-230-22.json by @vprusso (complete (3,8) template). Literature novelty is not claimed. Distance: a witness-backed upper bound (confidence upper_bound), d <= 40 (filed witnesses: X weight 41, Z weight 40; a weight-40 X logical seen in one run was not saved); nothing lighter in about 15.4 independent CPU-hours of Stern-type information-set decoding on both sides (39 runs in all, 21.4 CPU-hours; 15.4 after counting runs that repeat a seed in the second program once; two separate programs, our isd_fast with collision windows 16 and 14 and our isd_trace), lightest per side over all runs X 40, Z 40. No lower bound is claimed, so the true distance and score may be lower. Details in notes/994-142-40.md.
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

[[994,142,40]] — pair-partition CPM code on a 6 x 14 pair-closed template, weight-8 checks, rate 1/7, lift N = 71

Direction & hypothesis

Cell: CSS, unrestricted, weight 8, extended tier (n <= 1000 with w <= 8 and d <= 40). The pair-partition (PP) construction of Okada and Kasai (arXiv:2607.14091) gives CSS orthogonality from paired-difference equations on CPM exponents; they apply it to complete J x L templates. Lee, Okada, Maskara, Kasai and Zhou (arXiv:2609.30069) count the design rate as R = 1 - J_tot/L_stab and name quantum-compatible irregular templates as a natural direction. Our weight-8 entries so far use an irregular 5 x 12 template at rate 1/6 (codes/996-166-32.json, codes/996-166-34.json), and codes/996-166-36.json by @jacksongquera uses the same template.

Hypothesis: at weight 8 and n near 1000 a lower rate with more degree-4 columns can buy distance faster than it loses rate. A typical-distance estimate for the LDPC ensemble with the template's column-degree mix (the weight-distribution estimate of Gallager, Low-Density Parity-Check Codes, MIT Press 1963) puts a 6 x 14 pair-closed template (rate 1/7, 3 of 7 column pairs of degree 4) above the distance a rate-1/7 code needs to pass k d^2 / n = 216 at n = 994. This is an estimate, not a bound. This code: 142 * 40^2 / 994 = 228.6 (upper bound, from d <= 40); no lower bound is claimed.

Frontier: Among entries with max check weight <= 8 (and n <= 1000), the highest k d^2 / n on the board today is 216.0 (codes/996-166-36.json by @jacksongquera). This entry's is 228.6 as an upper bound (d <= 40). No lower bound is claimed, so the true score may be lower.

Technique (not ours): the pair-partition rule, its pairing arrays and the CPM lift are Okada and Kasai's (arXiv:2607.14091); the design-rate count and the permanent-vector upper bound (App. A of arXiv:2609.30069) are from Lee, Okada, Maskara, Kasai and Zhou (arXiv:2609.30069); quasi-cyclic CSS LDPC codes from circulant permutation matrices go back to Hagiwara and Imai (arXiv:quant-ph/0701020), and CSS pairs of two irregular LDPC codes were analysed by Hagiwara and Imai (arXiv:0801.1361).

Board precedents: the same commutation rule at weight 8: codes/996-166-36.json and codes/912-234-22.json by @jacksongquera, codes/904-230-22.json by @vprusso, our codes/996-166-32.json and codes/996-166-34.json. Literature novelty is not claimed.

What was searched

Template (the same on the X and the Z side). The 14 block columns form 7 column pairs {0,1}, ..., {12,13}; each of the 6 block rows is the union of 4 of the 7 pairs, so every check has weight 8 and every X-row / Z-row overlap is a union of whole pairs. Rows by pairs: [0,1,2,5], [0,2,3,5], [0,3,4,6], [1,3,5,6], [1,2,4,6], [0,1,2,4]: pairs {0,1}, {2,3}, {4,5} have qubit degree 4 and the other four pairs degree 3. Design rate 1 - 12/14 = 1/7. We enumerated the X = Z pair-closed 6 x 14 templates (33 classes with a permanent-vector ceiling, App. A of arXiv:2609.30069, of 48 or more) and searched each for pairings with our couple solver (a depth-first search for pairings whose exponent equations keep free dimensions), one cyclic symmetry of the template at a time, at least 3 free exponent dimensions and no forced parallel-column forms. Two classes had solutions; this template is the class whose solutions showed no built-in light logicals in a short screen. This pairing is one of the solutions with 3 free exponent dimensions found under an order-2 symmetry.

Lifts and triage. Random points of the solution space mod 71, 4-cycle free, k = 142 (= design) checked by rank, permanent-vector upper bound 52 for this draw (56 for the template). A short Stern screen (8 s per side) removed draws with a logical of weight 30 or less; the survivors entered a funnel that kills a code at its first logical of weight 38 or less (142 * 38^2 / 994 = 206.3 <= 216.0). Of the 40 lifts of this template class that entered the funnel, 29 showed a logical of weight 38 or less (28 of them within 0.4 to 2,045 s of search, one after 25,563 s), 3 passed 6 CPU-hours per side without one (this lift, whose search continued to the totals below, and two others still under check), and 8 were stopped undecided.

Evidence trail

Lightest non-trivial logical found for the submitted code, both sides (cumulative independent CPU, counting one run per side and seed):

| cumulative CPU-hours | search | lightest so far (both sides) | |---|---|---| | 0.17 | Stern ISD 600 s, X | 58 | | 0.33 | Stern ISD 600 s, Z | 49 | | 2.83 | Stern ISD 3600 s and 1800 s seeds, both sides | 48 | | 4.33 | Stern ISD 1800 s, X (a weight-40 X logical) | 40 | | 15.4 | 39 runs in all (21.4 CPU-h; 15.4 after counting same-seed repeats in the second program once), 97 to 3600 s, both sides | 40 |

Per side over all runs: X lightest 40, Z lightest 40. Filed witnesses: X weight 41 and Z weight 40. A weight-40 X logical was seen in one 1800 s run, which did not save its support, and a 1.5 h targeted search did not recover it; the filed X witness is the lightest saved one (41). The claim d <= 40 rests on the filed Z witness. Every filed witness was re-checked in a separate script: weight as reported, zero syndrome against the opposite checks, outside the row space of its own checks; the board's verify/qldpc_verify.py passes on the file.

Programs: our isd_fast (Stern, p = 2, collision windows 16 and 14) and our isd_trace (a second Stern implementation). Runs of the two programs with the same seed visit the same information sets, so they are counted once in the CPU figure (15.4 independent CPU-hours; 21.4 counting every run).

Claim: d <= 40, a witness-backed upper bound (confidence upper_bound). No lower bound is claimed; the search covers odd and even weights (odd-weight logicals occur in this template: 35, 37 and 39 were seen on other lifts), so a lighter logical may exist.

Dead ends

  • Template class 21 of the same shape: built-in light logicals (one qubit
  • on each column of 4 pairs, weight 8) in every lift.

  • 6 x 14 with X != Z, and 9 x 21 / 12 x 28 templates with a built-in cyclic
  • symmetry: no couple solutions with 3 or more free dimensions.

  • Our 5 x 12 template at n = 996: about 130 further lifts on 2026-10-28/29, all with
  • a logical of weight 36 or less.

Tools

Claude Opus 5.5 (Claude Code), unattended, for @MicheldeMessieres. Python and JavaScript for the builds and checks; our JavaScript couple solver (symmetry-orbit depth-first search with exact forced-form pruning); Stern information-set decoding (Stern 1989) in our C++ form (isd_fast, isd_trace). About 56.0 CPU-h for the template search (provenance.search_budget): about 50.5 CPU-h of Stern-type ISD over the 109 lifts that entered the funnel and about 5 CPU-h of couple search, lifts and 8 s screens of 815 lifts. Not counted: the distance checks of this code after the search (21.4 CPU-h counting every run, 15.4 independent).

Reproduction

N = 71, n = 994. H_X[i*N + r, c*N + ((r + S_X[i][c]) mod N)] = 1 for every block column c in X block row i (r = 0..70), and the same for H_Z with S_Z ('-' = empty cell):

S_X = [[62,40,7,40,37,52,-,-,-,-,27,27,-,-], [41,0,-,-,8,4,4,20,-,-,16,21,-,-], [49,32,-,-,-,-,31,33,33,16,-,-,6,65], [-,-,8,8,-,-,0,49,-,-,53,25,5,12], [-,-,29,15,70,0,-,-,69,9,-,-,7,38], [5,21,54,59,32,52,-,-,68,13,-,-,-,-]]

S_Z = [[9,63,25,63,47,67,-,-,-,-,37,42,-,-], [49,13,-,-,24,25,12,33,-,-,37,37,-,-], [17,66,-,-,-,-,70,67,42,25,-,-,23,11], [-,-,22,27,-,-,68,46,-,-,42,14,19,31], [-,-,32,13,10,6,-,-,4,20,-,-,10,36], [64,4,42,42,12,27,-,-,48,59,-,-,-,-]]

The pairing of each X-row / Z-row overlap is listed in provenance.construction; every pair (a, b) satisfies S_X[i][a] - S_Z[j][a] - S_X[i][b] + S_Z[j][b] = 0 (mod 71). rank H_X = rank H_Z = 426, so k = 994 - 852 = 142.

Parity checks

X-checks 426 (max weight 8) · Z-checks 426 (max weight 8)
H_X (426 checks, sparse supports)
[62, 111, 149, 253, 321, 407, 737, 808] [63, 112, 150, 254, 322, 408, 738, 809] [64, 113, 151, 255, 323, 409, 739, 810] [65, 114, 152, 256, 324, 410, 740, 811] [66, 115, 153, 257, 325, 411, 741, 812] [67, 116, 154, 258, 326, 412, 742, 813] [68, 117, 155, 259, 327, 413, 743, 814] [69, 118, 156, 260, 328, 414, 744, 815] [70, 119, 157, 261, 329, 415, 745, 816] [0, 120, 158, 262, 330, 416, 746, 817] [1, 121, 159, 263, 331, 417, 747, 818] [2, 122, 160, 264, 332, 418, 748, 819] [3, 123, 161, 265, 333, 419, 749, 820] [4, 124, 162, 266, 334, 420, 750, 821] [5, 125, 163, 267, 335, 421, 751, 822] [6, 126, 164, 268, 336, 422, 752, 823] [7, 127, 165, 269, 337, 423, 753, 824] [8, 128, 166, 270, 338, 424, 754, 825] [9, 129, 167, 271, 339, 425, 755, 826] [10, 130, 168, 272, 340, 355, 756, 827] [11, 131, 169, 273, 341, 356, 757, 828] [12, 132, 170, 274, 342, 357, 758, 829] [13, 133, 171, 275, 343, 358, 759, 830] [14, 134, 172, 276, 344, 359, 760, 831] [15, 135, 173, 277, 345, 360, 761, 832] [16, 136, 174, 278, 346, 361, 762, 833] [17, 137, 175, 279, 347, 362, 763, 834] [18, 138, 176, 280, 348, 363, 764, 835] [19, 139, 177, 281, 349, 364, 765, 836] [20, 140, 178, 282, 350, 365, 766, 837] [21, 141, 179, 283, 351, 366, 767, 838] [22, 71, 180, 213, 352, 367, 768, 839] [23, 72, 181, 214, 353, 368, 769, 840] [24, 73, 182, 215, 354, 369, 770, 841] [25, 74, 183, 216, 284, 370, 771, 842] [26, 75, 184, 217, 285, 371, 772, 843] [27, 76, 185, 218, 286, 372, 773, 844] [28, 77, 186, 219, 287, 373, 774, 845] [29, 78, 187, 220, 288, 374, 775, 846] [30, 79, 188, 221, 289, 375, 776, 847] [31, 80, 189, 222, 290, 376, 777, 848] [32, 81, 190, 223, 291, 377, 778, 849] [33, 82, 191, 224, 292, 378, 779, 850] [34, 83, 192, 225, 293, 379, 780, 851] [35, 84, 193, 226, 294, 380, 710, 781] [36, 85, 194, 227, 295, 381, 711, 782] [37, 86, 195, 228, 296, 382, 712, 783] [38, 87, 196, 229, 297, 383, 713, 784] [39, 88, 197, 230, 298, 384, 714, 785] [40, 89, 198, 231, 299, 385, 715, 786] [41, 90, 199, 232, 300, 386, 716, 787] [42, 91, 200, 233, 301, 387, 717, 788] [43, 92, 201, 234, 302, 388, 718, 789] [44, 93, 202, 235, 303, 389, 719, 790] [45, 94, 203, 236, 304, 390, 720, 791] [46, 95, 204, 237, 305, 391, 721, 792] [47, 96, 205, 238, 306, 392, 722, 793] [48, 97, 206, 239, 307, 393, 723, 794] [49, 98, 207, 240, 308, 394, 724, 795] [50, 99, 208, 241, 309, 395, 725, 796] [51, 100, 209, 242, 310, 396, 726, 797] [52, 101, 210, 243, 311, 397, 727, 798] [53, 102, 211, 244, 312, 398, 728, 799] [54, 103, 212, 245, 313, 399, 729, 800] [55, 104, 142, 246, 314, 400, 730, 801] [56, 105, 143, 247, 315, 401, 731, 802] [57, 106, 144, 248, 316, 402, 732, 803] [58, 107, 145, 249, 317, 403, 733, 804] [59, 108, 146, 250, 318, 404, 734, 805] [60, 109, 147, 251, 319, 405, 735, 806] [61, 110, 148, 252, 320, 406, 736, 807] [41, 71, 292, 359, 430, 517, 726, 802] [42, 72, 293, 360, 431, 518, 727, 803] [43, 73, 294, 361, 432, 519, 728, 804] [44, 74, 295, 362, 433, 520, 729, 805] [45, 75, 296, 363, 434, 521, 730, 806] [46, 76, 297, 364, 435, 522, 731, 807] [47, 77, 298, 365, 436, 523, 732, 808] [48, 78, 299, 366, 437, 524, 733, 809] [49, 79, 300, 367, 438, 525, 734, 810] [50, 80, 301, 368, 439, 526, 735, 811] [51, 81, 302, 369, 440, 527, 736, 812] [52, 82, 303, 370, 441, 528, 737, 813] [53, 83, 304, 371, 442, 529, 738, 814] [54, 84, 305, 372, 443, 530, 739, 815] [55, 85, 306, 373, 444, 531, 740, 816] [56, 86, 307, 374, 445, 532, 741, 817] [57, 87, 308, 375, 446, 533, 742, 818] [58, 88, 309, 376, 447, 534, 743, 819] [59, 89, 310, 377, 448, 535, 744, 820] [60, 90, 311, 378, 449, 536, 745, 821] [61, 91, 312, 379, 450, 537, 746, 822] [62, 92, 313, 380, 451, 538, 747, 823] [63, 93, 314, 381, 452, 539, 748, 824] [64, 94, 315, 382, 453, 540, 749, 825] [65, 95, 316, 383, 454, 541, 750, 826] [66, 96, 317, 384, 455, 542, 751, 827] [67, 97, 318, 385, 456, 543, 752, 828] [68, 98, 319, 386, 457, 544, 753, 829] [69, 99, 320, 387, 458, 545, 754, 830] [70, 100, 321, 388, 459, 546, 755, 831] [0, 101, 322, 389, 460, 547, 756, 832] [1, 102, 323, 390, 461, 548, 757, 833] [2, 103, 324, 391, 462, 549, 758, 834] [3, 104, 325, 392, 463, 550, 759, 835] [4, 105, 326, 393, 464, 551, 760, 836] [5, 106, 327, 394, 465, 552, 761, 837] [6, 107, 328, 395, 466, 553, 762, 838] [7, 108, 329, 396, 467, 554, 763, 839] [8, 109, 330, 397, 468, 555, 764, 840] [9, 110, 331, 398, 469, 556, 765, 841] [10, 111, 332, 399, 470, 557, 766, 842] [11, 112, 333, 400, 471, 558, 767, 843] [12, 113, 334, 401, 472, 559, 768, 844] [13, 114, 335, 402, 473, 560, 769, 845] [14, 115, 336, 403, 474, 561, 770, 846] [15, 116, 337, 404, 475, 562, 771, 847] [16, 117, 338, 405, 476, 563, 772, 848] [17, 118, 339, 406, 477, 564, 773, 849] [18, 119, 340, 407, 478, 565, 774, 850] [19, 120, 341, 408, 479, 566, 775, 851] [20, 121, 342, 409, 480, 567, 776, 781] [21, 122, 343, 410, 481, 497, 777, 782] [22, 123, 344, 411, 482, 498, 778, 783] [23, 124, 345, 412, 483, 499, 779, 784] [24, 125, 346, 413, 484, 500, 780, 785] [25, 126, 347, 414, 485, 501, 710, 786] [26, 127, 348, 415, 486, 502, 711, 787] [27, 128, 349, 416, 487, 503, 712, 788] [28, 129, 350, 417, 488, 504, 713, 789] [29, 130, 351, 418, 489, 505, 714, 790] [30, 131, 352, 419, 490, 506, 715, 791] [31, 132, 353, 420, 491, 507, 716, 792] [32, 133, 354, 421, 492, 508, 717, 793] [33, 134, 284, 422, 493, 509, 718, 794] [34, 135, 285, 423, 494, 510, 719, 795] [35, 136, 286, 424, 495, 511, 720, 796] [36, 137, 287, 425, 496, 512, 721, 797] [37, 138, 288, 355, 426, 513, 722, 798] [38, 139, 289, 356, 427, 514, 723, 799] [39, 140, 290, 357, 428, 515, 724, 800] [40, 141, 291, 358, 429, 516, 725, 801] [49, 103, 457, 530, 601, 655, 858, 988] [50, 104, 458, 531, 602, 656, 859, 989] [51, 105, 459, 532, 603, 657, 860, 990] [52, 106, 460, 533, 604, 658, 861, 991] [53, 107, 461, 534, 605, 659, 862, 992] [54, 108, 462, 535, 606, 660, 863, 993] [55, 109, 463, 536, 607, 661, 864, 923] [56, 110, 464, 537, 608, 662, 865, 924] [57, 111, 465, 538, 609, 663, 866, 925] [58, 112, 466, 539, 610, 664, 867, 926] [59, 113, 467, 540, 611, 665, 868, 927] [60, 114, 468, 541, 612, 666, 869, 928] [61, 115, 469, 542, 613, 667, 870, 929] [62, 116, 470, 543, 614, 668, 871, 930] [63, 117, 471, 544, 615, 669, 872, 931] [64, 118, 472, 545, 616, 670, 873, 932] [65, 119, 473, 546, 617, 671, 874, 933] [66, 120, 474, 547, 618, 672, 875, 934] [67, 121, 475, 548, 619, 673, 876, 935] [68, 122, 476, 549, 620, 674, 877, 936] [69, 123, 477, 550, 621, 675, 878, 937] [70, 124, 478, 551, 622, 676, 879, 938] [0, 125, 479, 552, 623, 677, 880, 939] [1, 126, 480, 553, 624, 678, 881, 940] [2, 127, 481, 554, 625, 679, 882, 941] [3, 128, 482, 555, 626, 680, 883, 942] [4, 129, 483, 556, 627, 681, 884, 943] [5, 130, 484, 557, 628, 682, 885, 944] [6, 131, 485, 558, 629, 683, 886, 945] [7, 132, 486, 559, 630, 684, 887, 946] [8, 133, 487, 560, 631, 685, 888, 947] [9, 134, 488, 561, 632, 686, 889, 948] [10, 135, 489, 562, 633, 687, 890, 949] [11, 136, 490, 563, 634, 688, 891, 950] [12, 137, 491, 564, 635, 689, 892, 951] [13, 138, 492, 565, 636, 690, 893, 952] [14, 139, 493, 566, 637, 691, 894, 953] [15, 140, 494, 567, 638, 692, 895, 954] [16, 141, 495, 497, 568, 693, 896, 955] [17, 71, 496, 498, 569, 694, 897, 956] [18, 72, 426, 499, 570, 695, 898, 957] [19, 73, 427, 500, 571, 696, 899, 958] [20, 74, 428, 501, 572, 697, 900, 959] [21, 75, 429, 502, 573, 698, 901, 960] [22, 76, 430, 503, 574, 699, 902, 961] [23, 77, 431, 504, 575, 700, 903, 962] [24, 78, 432, 505, 576, 701, 904, 963] [25, 79, 433, 506, 577, 702, 905, 964] [26, 80, 434, 507, 578, 703, 906, 965] [27, 81, 435, 508, 579, 704, 907, 966] [28, 82, 436, 509, 580, 705, 908, 967] [29, 83, 437, 510, 581, 706, 909, 968] [30, 84, 438, 511, 582, 707, 910, 969] [31, 85, 439, 512, 583, 708, 911, 970] [32, 86, 440, 513, 584, 709, 912, 971] [33, 87, 441, 514, 585, 639, 913, 972] [34, 88, 442, 515, 586, 640, 914, 973] [35, 89, 443, 516, 587, 641, 915, 974] [36, 90, 444, 517, 588, 642, 916, 975] [37, 91, 445, 518, 589, 643, 917, 976] [38, 92, 446, 519, 590, 644, 918, 977] [39, 93, 447, 520, 591, 645, 919, 978] [40, 94, 448, 521, 592, 646, 920, 979] [41, 95, 449, 522, 593, 647, 921, 980] [42, 96, 450, 523, 594, 648, 922, 981] [43, 97, 451, 524, 595, 649, 852, 982] [44, 98, 452, 525, 596, 650, 853, 983] [45, 99, 453, 526, 597, 651, 854, 984] [46, 100, 454, 527, 598, 652, 855, 985] [47, 101, 455, 528, 599, 653, 856, 986] [48, 102, 456, 529, 600, 654, 857, 987] [150, 221, 426, 546, 763, 806, 857, 935] [151, 222, 427, 547, 764, 807, 858, 936] [152, 223, 428, 548, 765, 808, 859, 937] [153, 224, 429, 549, 766, 809, 860, 938] [154, 225, 430, 550, 767, 810, 861, 939] [155, 226, 431, 551, 768, 811, 862, 940] [156, 227, 432, 552, 769, 812, 863, 941] [157, 228, 433, 553, 770, 813, 864, 942] [158, 229, 434, 554, 771, 814, 865, 943] [159, 230, 435, 555, 772, 815, 866, 944] [160, 231, 436, 556, 773, 816, 867, 945] [161, 232, 437, 557, 774, 817, 868, 946] [162, 233, 438, 558, 775, 818, 869, 947] [163, 234, 439, 559, 776, 819, 870, 948] [164, 235, 440, 560, 777, 820, 871, 949] [165, 236, 441, 561, 778, 821, 872, 950] [166, 237, 442, 562, 779, 822, 873, 951] [167, 238, 443, 563, 780, 823, 874, 952] [168, 239, 444, 564, 710, 824, 875, 953] [169, 240, 445, 565, 711, 825, 876, 954] [170, 241, 446, 566, 712, 826, 877, 955] [171, 242, 447, 567, 713, 827, 878, 956] [172, 243, 448, 497, 714, 828, 879, 957] [173, 244, 449, 498, 715, 829, 880, 958] [174, 245, 450, 499, 716, 830, 881, 959] [175, 246, 451, 500, 717, 831, 882, 960] [176, 247, 452, 501, 718, 832, 883, 961] [177, 248, 453, 502, 719, 833, 884, 962] [178, 249, 454, 503, 720, 834, 885, 963] [179, 250, 455, 504, 721, 835, 886, 964] [180, 251, 456, 505, 722, 836, 887, 965] [181, 252, 457, 506, 723, 837, 888, 966] [182, 253, 458, 507, 724, 838, 889, 967] [183, 254, 459, 508, 725, 839, 890, 968] [184, 255, 460, 509, 726, 840, 891, 969] [185, 256, 461, 510, 727, 841, 892, 970] [186, 257, 462, 511, 728, 842, 893, 971] [187, 258, 463, 512, 729, 843, 894, 972] [188, 259, 464, 513, 730, 844, 895, 973] [189, 260, 465, 514, 731, 845, 896, 974] [190, 261, 466, 515, 732, 846, 897, 975] [191, 262, 467, 516, 733, 847, 898, 976] [192, 263, 468, 517, 734, 848, 899, 977] [193, 264, 469, 518, 735, 849, 900, 978] [194, 265, 470, 519, 736, 850, 901, 979] [195, 266, 471, 520, 737, 851, 902, 980] [196, 267, 472, 521, 738, 781, 903, 981] [197, 268, 473, 522, 739, 782, 904, 982] [198, 269, 474, 523, 740, 783, 905, 983] [199, 270, 475, 524, 741, 784, 906, 984] [200, 271, 476, 525, 742, 785, 907, 985] [201, 272, 477, 526, 743, 786, 908, 986] [202, 273, 478, 527, 744, 787, 909, 987] [203, 274, 479, 528, 745, 788, 910, 988] [204, 275, 480, 529, 746, 789, 911, 989] [205, 276, 481, 530, 747, 790, 912, 990] [206, 277, 482, 531, 748, 791, 913, 991] [207, 278, 483, 532, 749, 792, 914, 992] [208, 279, 484, 533, 750, 793, 915, 993] [209, 280, 485, 534, 751, 794, 916, 923] [210, 281, 486, 535, 752, 795, 917, 924] [211, 282, 487, 536, 753, 796, 918, 925] [212, 283, 488, 537, 754, 797, 919, 926] [142, 213, 489, 538, 755, 798, 920, 927] [143, 214, 490, 539, 756, 799, 921, 928] [144, 215, 491, 540, 757, 800, 922, 929] [145, 216, 492, 541, 758, 801, 852, 930] [146, 217, 493, 542, 759, 802, 853, 931] [147, 218, 494, 543, 760, 803, 854, 932] [148, 219, 495, 544, 761, 804, 855, 933] [149, 220, 496, 545, 762, 805, 856, 934] [171, 228, 354, 355, 637, 648, 859, 961] [172, 229, 284, 356, 638, 649, 860, 962] [173, 230, 285, 357, 568, 650, 861, 963] [174, 231, 286, 358, 569, 651, 862, 964] [175, 232, 287, 359, 570, 652, 863, 965] [176, 233, 288, 360, 571, 653, 864, 966] [177, 234, 289, 361, 572, 654, 865, 967] [178, 235, 290, 362, 573, 655, 866, 968] [179, 236, 291, 363, 574, 656, 867, 969] [180, 237, 292, 364, 575, 657, 868, 970] [181, 238, 293, 365, 576, 658, 869, 971] [182, 239, 294, 366, 577, 659, 870, 972] [183, 240, 295, 367, 578, 660, 871, 973] [184, 241, 296, 368, 579, 661, 872, 974] [185, 242, 297, 369, 580, 662, 873, 975] [186, 243, 298, 370, 581, 663, 874, 976] [187, 244, 299, 371, 582, 664, 875, 977] [188, 245, 300, 372, 583, 665, 876, 978] [189, 246, 301, 373, 584, 666, 877, 979] [190, 247, 302, 374, 585, 667, 878, 980] [191, 248, 303, 375, 586, 668, 879, 981] [192, 249, 304, 376, 587, 669, 880, 982] [193, 250, 305, 377, 588, 670, 881, 983] [194, 251, 306, 378, 589, 671, 882, 984] [195, 252, 307, 379, 590, 672, 883, 985] [196, 253, 308, 380, 591, 673, 884, 986] [197, 254, 309, 381, 592, 674, 885, 987] [198, 255, 310, 382, 593, 675, 886, 988] [199, 256, 311, 383, 594, 676, 887, 989] [200, 257, 312, 384, 595, 677, 888, 990] [201, 258, 313, 385, 596, 678, 889, 991] [202, 259, 314, 386, 597, 679, 890, 992] [203, 260, 315, 387, 598, 680, 891, 993] [204, 261, 316, 388, 599, 681, 892, 923] [205, 262, 317, 389, 600, 682, 893, 924] [206, 263, 318, 390, 601, 683, 894, 925] [207, 264, 319, 391, 602, 684, 895, 926] [208, 265, 320, 392, 603, 685, 896, 927] [209, 266, 321, 393, 604, 686, 897, 928] [210, 267, 322, 394, 605, 687, 898, 929] [211, 268, 323, 395, 606, 688, 899, 930] [212, 269, 324, 396, 607, 689, 900, 931] [142, 270, 325, 397, 608, 690, 901, 932] [143, 271, 326, 398, 609, 691, 902, 933] [144, 272, 327, 399, 610, 692, 903, 934] [145, 273, 328, 400, 611, 693, 904, 935] [146, 274, 329, 401, 612, 694, 905, 936] [147, 275, 330, 402, 613, 695, 906, 937] [148, 276, 331, 403, 614, 696, 907, 938] [149, 277, 332, 404, 615, 697, 908, 939] [150, 278, 333, 405, 616, 698, 909, 940] [151, 279, 334, 406, 617, 699, 910, 941] [152, 280, 335, 407, 618, 700, 911, 942] [153, 281, 336, 408, 619, 701, 912, 943] [154, 282, 337, 409, 620, 702, 913, 944] [155, 283, 338, 410, 621, 703, 914, 945] [156, 213, 339, 411, 622, 704, 915, 946] [157, 214, 340, 412, 623, 705, 916, 947] [158, 215, 341, 413, 624, 706, 917, 948] [159, 216, 342, 414, 625, 707, 918, 949] [160, 217, 343, 415, 626, 708, 919, 950] [161, 218, 344, 416, 627, 709, 920, 951] [162, 219, 345, 417, 628, 639, 921, 952] [163, 220, 346, 418, 629, 640, 922, 953] [164, 221, 347, 419, 630, 641, 852, 954] [165, 222, 348, 420, 631, 642, 853, 955] [166, 223, 349, 421, 632, 643, 854, 956] [167, 224, 350, 422, 633, 644, 855, 957] [168, 225, 351, 423, 634, 645, 856, 958] [169, 226, 352, 424, 635, 646, 857, 959] [170, 227, 353, 425, 636, 647, 858, 960] [5, 92, 196, 272, 316, 407, 636, 652] [6, 93, 197, 273, 317, 408, 637, 653] [7, 94, 198, 274, 318, 409, 638, 654] [8, 95, 199, 275, 319, 410, 568, 655] [9, 96, 200, 276, 320, 411, 569, 656] [10, 97, 201, 277, 321, 412, 570, 657] [11, 98, 202, 278, 322, 413, 571, 658] [12, 99, 203, 279, 323, 414, 572, 659] [13, 100, 204, 280, 324, 415, 573, 660] [14, 101, 205, 281, 325, 416, 574, 661] [15, 102, 206, 282, 326, 417, 575, 662] [16, 103, 207, 283, 327, 418, 576, 663] [17, 104, 208, 213, 328, 419, 577, 664] [18, 105, 209, 214, 329, 420, 578, 665] [19, 106, 210, 215, 330, 421, 579, 666] [20, 107, 211, 216, 331, 422, 580, 667] [21, 108, 212, 217, 332, 423, 581, 668] [22, 109, 142, 218, 333, 424, 582, 669] [23, 110, 143, 219, 334, 425, 583, 670] [24, 111, 144, 220, 335, 355, 584, 671] [25, 112, 145, 221, 336, 356, 585, 672] [26, 113, 146, 222, 337, 357, 586, 673] [27, 114, 147, 223, 338, 358, 587, 674] [28, 115, 148, 224, 339, 359, 588, 675] [29, 116, 149, 225, 340, 360, 589, 676] [30, 117, 150, 226, 341, 361, 590, 677] [31, 118, 151, 227, 342, 362, 591, 678] [32, 119, 152, 228, 343, 363, 592, 679] [33, 120, 153, 229, 344, 364, 593, 680] [34, 121, 154, 230, 345, 365, 594, 681] [35, 122, 155, 231, 346, 366, 595, 682] [36, 123, 156, 232, 347, 367, 596, 683] [37, 124, 157, 233, 348, 368, 597, 684] [38, 125, 158, 234, 349, 369, 598, 685] [39, 126, 159, 235, 350, 370, 599, 686] [40, 127, 160, 236, 351, 371, 600, 687] [41, 128, 161, 237, 352, 372, 601, 688] [42, 129, 162, 238, 353, 373, 602, 689] [43, 130, 163, 239, 354, 374, 603, 690] [44, 131, 164, 240, 284, 375, 604, 691] [45, 132, 165, 241, 285, 376, 605, 692] [46, 133, 166, 242, 286, 377, 606, 693] [47, 134, 167, 243, 287, 378, 607, 694] [48, 135, 168, 244, 288, 379, 608, 695] [49, 136, 169, 245, 289, 380, 609, 696] [50, 137, 170, 246, 290, 381, 610, 697] [51, 138, 171, 247, 291, 382, 611, 698] [52, 139, 172, 248, 292, 383, 612, 699] [53, 140, 173, 249, 293, 384, 613, 700] [54, 141, 174, 250, 294, 385, 614, 701] [55, 71, 175, 251, 295, 386, 615, 702] [56, 72, 176, 252, 296, 387, 616, 703] [57, 73, 177, 253, 297, 388, 617, 704] [58, 74, 178, 254, 298, 389, 618, 705] [59, 75, 179, 255, 299, 390, 619, 706] [60, 76, 180, 256, 300, 391, 620, 707] [61, 77, 181, 257, 301, 392, 621, 708] [62, 78, 182, 258, 302, 393, 622, 709] [63, 79, 183, 259, 303, 394, 623, 639] [64, 80, 184, 260, 304, 395, 624, 640] [65, 81, 185, 261, 305, 396, 625, 641] [66, 82, 186, 262, 306, 397, 626, 642] [67, 83, 187, 263, 307, 398, 627, 643] [68, 84, 188, 264, 308, 399, 628, 644] [69, 85, 189, 265, 309, 400, 629, 645] [70, 86, 190, 266, 310, 401, 630, 646] [0, 87, 191, 267, 311, 402, 631, 647] [1, 88, 192, 268, 312, 403, 632, 648] [2, 89, 193, 269, 313, 404, 633, 649] [3, 90, 194, 270, 314, 405, 634, 650] [4, 91, 195, 271, 315, 406, 635, 651]
H_Z (426 checks, sparse supports)
[9, 134, 167, 276, 331, 422, 747, 823] [10, 135, 168, 277, 332, 423, 748, 824] [11, 136, 169, 278, 333, 424, 749, 825] [12, 137, 170, 279, 334, 425, 750, 826] [13, 138, 171, 280, 335, 355, 751, 827] [14, 139, 172, 281, 336, 356, 752, 828] [15, 140, 173, 282, 337, 357, 753, 829] [16, 141, 174, 283, 338, 358, 754, 830] [17, 71, 175, 213, 339, 359, 755, 831] [18, 72, 176, 214, 340, 360, 756, 832] [19, 73, 177, 215, 341, 361, 757, 833] [20, 74, 178, 216, 342, 362, 758, 834] [21, 75, 179, 217, 343, 363, 759, 835] [22, 76, 180, 218, 344, 364, 760, 836] [23, 77, 181, 219, 345, 365, 761, 837] [24, 78, 182, 220, 346, 366, 762, 838] [25, 79, 183, 221, 347, 367, 763, 839] [26, 80, 184, 222, 348, 368, 764, 840] [27, 81, 185, 223, 349, 369, 765, 841] [28, 82, 186, 224, 350, 370, 766, 842] [29, 83, 187, 225, 351, 371, 767, 843] [30, 84, 188, 226, 352, 372, 768, 844] [31, 85, 189, 227, 353, 373, 769, 845] [32, 86, 190, 228, 354, 374, 770, 846] [33, 87, 191, 229, 284, 375, 771, 847] [34, 88, 192, 230, 285, 376, 772, 848] [35, 89, 193, 231, 286, 377, 773, 849] [36, 90, 194, 232, 287, 378, 774, 850] [37, 91, 195, 233, 288, 379, 775, 851] [38, 92, 196, 234, 289, 380, 776, 781] [39, 93, 197, 235, 290, 381, 777, 782] [40, 94, 198, 236, 291, 382, 778, 783] [41, 95, 199, 237, 292, 383, 779, 784] [42, 96, 200, 238, 293, 384, 780, 785] [43, 97, 201, 239, 294, 385, 710, 786] [44, 98, 202, 240, 295, 386, 711, 787] [45, 99, 203, 241, 296, 387, 712, 788] [46, 100, 204, 242, 297, 388, 713, 789] [47, 101, 205, 243, 298, 389, 714, 790] [48, 102, 206, 244, 299, 390, 715, 791] [49, 103, 207, 245, 300, 391, 716, 792] [50, 104, 208, 246, 301, 392, 717, 793] [51, 105, 209, 247, 302, 393, 718, 794] [52, 106, 210, 248, 303, 394, 719, 795] [53, 107, 211, 249, 304, 395, 720, 796] [54, 108, 212, 250, 305, 396, 721, 797] [55, 109, 142, 251, 306, 397, 722, 798] [56, 110, 143, 252, 307, 398, 723, 799] [57, 111, 144, 253, 308, 399, 724, 800] [58, 112, 145, 254, 309, 400, 725, 801] [59, 113, 146, 255, 310, 401, 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[38, 120, 158, 229, 341, 356, 590, 672] [39, 121, 159, 230, 342, 357, 591, 673] [40, 122, 160, 231, 343, 358, 592, 674] [41, 123, 161, 232, 344, 359, 593, 675] [42, 124, 162, 233, 345, 360, 594, 676] [43, 125, 163, 234, 346, 361, 595, 677] [44, 126, 164, 235, 347, 362, 596, 678] [45, 127, 165, 236, 348, 363, 597, 679] [46, 128, 166, 237, 349, 364, 598, 680] [47, 129, 167, 238, 350, 365, 599, 681] [48, 130, 168, 239, 351, 366, 600, 682] [49, 131, 169, 240, 352, 367, 601, 683] [50, 132, 170, 241, 353, 368, 602, 684] [51, 133, 171, 242, 354, 369, 603, 685] [52, 134, 172, 243, 284, 370, 604, 686] [53, 135, 173, 244, 285, 371, 605, 687] [54, 136, 174, 245, 286, 372, 606, 688] [55, 137, 175, 246, 287, 373, 607, 689] [56, 138, 176, 247, 288, 374, 608, 690] [57, 139, 177, 248, 289, 375, 609, 691] [58, 140, 178, 249, 290, 376, 610, 692] [59, 141, 179, 250, 291, 377, 611, 693] [60, 71, 180, 251, 292, 378, 612, 694] [61, 72, 181, 252, 293, 379, 613, 695] [62, 73, 182, 253, 294, 380, 614, 696] [63, 74, 183, 254, 295, 381, 615, 697]
Code ID 994-142-40 · download JSON · raw on GitHub