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[[944,32,24]] d ≤
n
944
k
32
d
24
kd²/n
19.525
w
7
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 24, d_Z ≤ 24 · w_X = 7, w_Z = 7 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 24 · witness weight 24 (claimed upper_bound)
witness operator (support, 24 qubits)
[32, 33, 36, 37, 44, 45, 104, 105, 304, 305, 308, 309, 324, 325, 332, 333, 432, 433, 488, 489, 544, 545, 616, 617]
d_Z 24 · witness weight 24 (claimed upper_bound)
witness operator (support, 24 qubits)
[28, 29, 224, 225, 236, 237, 256, 257, 288, 289, 336, 337, 364, 365, 460, 461, 512, 513, 576, 577, 604, 605, 616, 617]
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 5–7 (mean 6.912) · H_Z 5–7 (mean 6.912)
qubit degrees H_X 2–6 (mean 3.983) · H_Z 2–6 (mean 3.983)
trapping sets H_X (1,2)×8 (2,2)×12 (3,2)×12 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 8 (1,3): 176 (1,4): 672 (1,6): 88 (2,2): 12 (2,4): 440 (2,5): 1856 (2,6): 6256 (2,7): 472 (2,8): 1620 (2,10): 484 (3,2): 12 (3,4): 668 (3,5): 960 (3,6): 11048 (3,7): 30496 (3,8): 82706 (3,9): 17056 (3,10): 40804 (3,11): 4312 (3,12): 17388 (3,13): 416 (3,14): 5716 (3,16): 148
trapping sets H_Z (1,2)×16 (2,2)×24 (3,2)×24 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 16 (1,3): 160 (1,4): 680 (1,6): 88 (2,2): 24 (2,3): 16 (2,4): 424 (2,5): 1696 (2,6): 6432 (2,7): 416 (2,8): 1648 (2,10): 482 (3,2): 24 (3,3): 48 (3,4): 748 (3,5): 1012 (3,6): 10636 (3,7): 28348 (3,8): 85804 (3,9): 15136 (3,10): 42488 (3,11): 3784 (3,12): 17662 (3,13): 356 (3,14): 5694 (3,16): 146

Construction & provenance

authors @MathysRennela
provenance submitted through the challenge
novelty novelty not audited
construction One [[4,2,2]] distance-amplification step (CSS tensor product, central three-term truncation, arXiv:2609.37231 Eq. 1/Eq. 12-15) applied to the board's [[192,16,12]] entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 944, k' = 2k = 32, w' = w+1 = 7. X/Z witnesses are the base witnesses tensored with the weight-2 [[4,2,2]] logical on the central register (weights 24/24); the doubled distance is certified by the logical-overlap criterion (d' >= 2d) and no lighter logical was found in a 100,000-trial accelerator search on the first-tier candidates of the same family. Base provenance: contributed via qldpc submit
model Space Bunny Alpha 1.0 (claimed, not verified)
builds on arXiv:2609.37231
date 2026-09-30
notes Constructed and packaged with the Space Bunny Alpha 1.0 model.
family distance-amplified (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

[[944,32,24]] — one [[4,2,2]] distance-amplification step of [[192,16,12]]

Direction & hypothesis

Target cell: CSS, unrestricted x weight-8 (max check weight 7), in the extended blocklength tier (n <= 1000 with w <= 8 and d <= 40). Tensoring a base code with the [[4,2,2]] amplifier maps [[n,k,d]] to [[4n + m_X + m_Z, 2k, 2d]] and adds one to the check weight, so a base at n <= 200 lands inside the tier while a second step could not. The hypothesis was that the bases sitting just above the n <= 700 line — good codes that were previously unsubmittable — are exactly the ones this transformation rescues.

What was searched

Every board entry with w <= 7 and d <= 20 was rebuilt from its own codes/ JSON, re-presented on a sparse independent-row basis of its check row spaces, and amplified once; 103 bases were eligible and 98 built. Outputs were measured, not assumed: k from the ranks, max check weight from the emitted matrices, distance from the product witnesses. Survivors are those no board entry dominates on (n, k, d, w). Eleven advanced; they are submitted as a family.

Evidence trail

The X and Z witnesses are the base entry's witnesses tensored with the weight-2 [[4,2,2]] logical on the central (data-data) register, weights 24 / 24 here. Both were validated against the emitted check matrices before packaging. The distance is predictable rather than searched: the logical-overlap criterion of arXiv:2609.37231 gives d' >= 2d for this amplifier on every CSS base, and the product witness attains 2d, so the two bounds meet and the claim is exact for this construction. verify/validate_candidate.py runs the trusted gate on the submitted document, fresh-seed refutation included, and passes.

Dead ends

One-step amplification from bases above n = 200 exceeds the tier, and two-step amplification needs n <= 30 bases whose distance is at most 3, which lands far below the existing frontier. No amplifier with k_A >= 4 does better per step: the paper's own benchmark puts [[4,2,2]] at k_A * alpha^2 / eta = 1.60, against 0.54-0.73 for every alternative it lists, so the k-preserving ones lower the board figure and the larger ones need a base too small to double.

Tools

Model: Space Bunny Alpha 1.0 (agent), driving the repo's own tooling: Python with numpy, schema/code.schema.json for the document shape, verify/validate_candidate.py for the gate, and research/kit/submit.py for packaging. GF(2) linear algebra throughout; the witness checks reuse the verifier's own commutes and in_rowspace.

Reproduction

Take the base entry codes/192-16-12.json. Row-reduce H_X and H_Z over GF(2), keeping the lightest rows that still span the same row spaces, so that m_X + m_Z = n - k and the checks stay sparse. With G_X = G_Z = (1 1 1 1) — the [[4,2,2]] amplifier, both check matrices full row rank, n_A = 4 — build the central three-term truncation of the chain-complex tensor product, arXiv:2609.37231 Eq. 14-15, with the column blocks ordered (Q_1 ⊗ A_1, Q_2 ⊗ A_0, Q_0 ⊗ A_2):

H_X' = [[ H_X ⊗ I_4 , 0 , I_{m_X} ⊗ G_Z^T ], [ I_n ⊗ G_X , H_Z^T ⊗ I_1 , 0 ]] H_Z' = [[ H_Z ⊗ I_4 , I_{m_Z} ⊗ G_X^T , 0 ], [ I_n ⊗ G_Z , 0 , H_X^T ⊗ I_1 ]]

Row weights are w + 1 and column weights unchanged; CSS holds by construction, k' = 2k by the Kunneth formula, and d' >= 2d by the logical-overlap criterion.

Parity checks

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