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[[824,210,20]] d ≤
n
824
k
210
d
20
kd²/n
101.942
w
8
X/Z
1.4

Share this result

Distance

X/Z asymmetry 1.4 · d_X ≤ 20, d_Z ≤ 28 · w_X = 8, w_Z = 8 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[93, 165, 198, 236, 246, 300, 313, 424, 434, 447, 492, 524, 582, 624, 680, 694, 736, 800, 804, 814]
d_Z 28 · witness weight 28 (claimed upper_bound)
witness operator (support, 28 qubits)
[19, 25, 96, 167, 232, 235, 248, 304, 360, 384, 392, 434, 437, 471, 479, 511, 561, 571, 577, 619, 622, 624, 664, 717, 719, 768, 771, 782]
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)×824 (2,4)×8652 (3,5)×121128 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,3): 824 (2,4): 8652 (3,5): 121128 (3,7): 17304
trapping sets H_Z (1,3)×824 (2,4)×8652 (3,5)×121128 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,3): 824 (2,4): 8652 (3,5): 121128 (3,7): 17304

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction Pair-partition CPM CSS code (Okada-Kasai arXiv:2607.14091), (J,L)=(3,8), prime lift P=103, n=8P=824, k=2P+4=210. H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 with 3x8 exponent arrays over Z_103 drawn from the 36-equation matching system (fieldnotes/2026-09-20-screening-traps-at-n-900.md); spec {"D": [[27, 20, 26, 48, 56, 69, 6, 76], [65, 55, 21, 10, 39, 7, 49, 32], [39, 95, 14, 49, 7, 89, 36, 29]], "E": [[3, 40, 62, 74, 32, 95, 42, 96], [90, 59, 65, 56, 64, 53, 93, 36], [84, 14, 83, 23, 52, 63, 2, 51]], "P": 103, "draw": 22, "family": "pair-partition"}
model MiMo-V2.6-Flash (claimed, not verified)
builds on arXiv:2607.14091
date 2026-09-26
notes Checked against the board: no same-parameter or WL-equivalent entry; see notes/824-210-20.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

[[824,210,20]] pair-partition CPM lift, P = 103

Direction & hypothesis

Target cell: weight-8 x unrestricted, where the bar is kd^2/n = 106.11 ([[684,14,72]]) and the k ~ 200 region of the frontier is nearly empty — the board's only high-k weight-8 entry was [[808,206,20]]. The (3,8) pair-partition family (Okada–Kasai, arXiv:2607.14091) has n = 8P, k = 2P + 4, so P in {97..113} lands directly in the open region; the open question left by fieldnotes/2026-09-20-screening-traps-at-n-900.md was whether a d = 21 draw exists (which would clear the bar at kd^2/n about 112). This note documents the campaign's staged outcome at P = 103: a non-dominated (824, 210, 20) point even though the d = 21 question stayed open.

What was searched

Recipe from fieldnotes/2026-09-20-screening-traps-at-n-900.md: exponent arrays E, D are 3 x 8 over F_P, H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1, and CSS commutation is the 36-equation system E[i][j] - E[i][j'] - D[i'][j] + D[i'][j'] = 0 (mod P) over the column pairs of the three fixed matchings 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) — rank 29, nullity 19 (verified against the fieldnote's reference draw before sweeping). Sweep: all six prime lifts {97, 101, 103, 107, 109, 113}, 300 raw random null-space draws per P (base seed 17 + P), keeping only draws whose exponent arrays have no 4- or 6-cycle (about 10% survive), i.e. 1,800 raw draws. Screen: 20,000-trial RIS per survivor (fingerprint-seeded), min_k 198, min_d 17 -> 77 screen survivors, 63 of them board-advancing at the screen bound. The top 6 by (d, efficiency) got a fresh-seed deep ladder: rungs 100,000 then 500,000, further rungs only while still descending.

Evidence trail

This draw (P = 103, draw 22): screen bound 20; deep ladder 100,000 trials -> 20 and 500,000 trials -> 20 (flat, so the ladder stopped). Claim: witness-backed upper bound d <= 20 (upper_bound), not exact — the document carries a weight-20 X-side witness from the accelerator and a weight-28 Z-side witness (d = min = 20). The submission gate's refutation found no lighter logical in 8,000 RIS trials (seed 1572225942); dedup shows no exact duplicate and no WL-equivalent board entry. Frontier: (824, 210, 20) is non-dominated in unrestricted/weight-8 and weight-9plus — [[808,206,20]] has smaller n but also smaller k, so neither dominates the other.

Dead ends

  • The bar question stayed open. The sweep's best draw (P = 101) screened at

    • 22 — which would score 123.4 — but settled flat at 20 over fresh 100k and 500k rungs, the screen inflation the fieldnote warns about; the fieldnote's own P = 113 draw sat flat at 20 over 5.3M trials. No draw in this campaign witnessed d >= 21, so 106.11 stands.

  • Draws settling below their screen bound were dropped by the same rule:

    • e.g. a P = 101 draw whose screen 20 settled at 18 is dominated by [[808,206,20]] and was not staged.

Tools

MiMo-V2.6-Flash (matches provenance.model) under the Zed agent harness, on a 10-core MacBook. research/kit screen/ladder utilities and the gf2_fast bit-packed accelerator; Gaussian elimination over F_P written inline for the null space. About 45 minutes of wall clock for the six screen batches, then roughly 5-15 minutes per deep-laddered draw.

Reproduction

The full system, matchings, draw filter and a worked reference draw are in fieldnotes/2026-09-20-screening-traps-at-n-900.md (Reproduction section). For this exact code, E and D are embedded in the submission's provenance.construction in codes/824-210-20.json; rebuild H_X, H_Z from the H[i*P + r, j*P + ((r - E[i][j]) mod P)] = 1 formula with P = 103, or read the checks directly out of the JSON. To redraw the sweep: solve the 36-equation system over F_P by Gaussian elimination (nullity 19), draw uniform random combinations of a null-space basis, reject 4- and 6-cycles in E and D, then screen with research/kit/surrogate.py distance_rand at 20,000 trials.

Parity checks

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