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[[834,32,20]] d ≤
n
834
k
32
d
20
kd²/n
15.348
w
7
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 20, d_Z ≤ 20 · 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 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[4, 5, 76, 77, 136, 137, 168, 169, 248, 249, 388, 389, 396, 397, 416, 417, 440, 441, 628, 629]
d_Z 20 · witness weight 20 (claimed upper_bound)
witness operator (support, 20 qubits)
[116, 117, 408, 409, 420, 421, 480, 481, 496, 497, 552, 553, 556, 557, 616, 617, 628, 629, 676, 677]
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 6.9) · H_Z 5–7 (mean 6.9)
qubit degrees H_X 2–6 (mean 3.954) · H_Z 2–6 (mean 3.954)
trapping sets H_X (1,2)×4 (2,2)×6 (3,2)×6 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,2): 4 (1,3): 184 (1,4): 569 (1,6): 77 (2,2): 6 (2,4): 452 (2,5): 1904 (2,6): 5138 (2,7): 528 (2,8): 1308 (2,10): 415 (3,2): 6 (3,4): 620 (3,5): 1228 (3,6): 11254 (3,7): 29936 (3,8): 66350 (3,9): 17668 (3,10): 31880 (3,11): 4656 (3,12): 13937 (3,13): 504 (3,14): 4493 (3,16): 123
trapping sets H_Z (1,2)×4 (2,2)×6 (3,2)×6 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,2): 4 (1,3): 184 (1,4): 569 (1,6): 77 (2,2): 6 (2,3): 4 (2,4): 440 (2,5): 1916 (2,6): 5134 (2,7): 528 (2,8): 1308 (2,10): 415 (3,2): 6 (3,3): 12 (3,4): 620 (3,5): 1208 (3,6): 11122 (3,7): 30260 (3,8): 66026 (3,9): 17872 (3,10): 31820 (3,11): 4664 (3,12): 13925 (3,13): 504 (3,14): 4493 (3,16): 123

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 [[170,16,10]] weight-6 two-block generalized bicycle on Z_85 entry, using a sparse independent-row presentation of its checks: n' = 4n + m_X + m_Z = 834, 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 20/20); 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: Generalized bicycle (two-block) code on Z_85: H_X=[A|B], H_Z=[B^T|A^T], a(x)=x8+x33+x46, b(x)=x3+x18+x70; g=gcd(a,b,x85-1) irreducible of degree 8, k=2*deg(g)=16, row weight 6. Full circulant check sets kept (redundant rows carry the symmetry).
model Space Bunny Alpha 1.0 (claimed, not verified)
builds on arXiv:2609.37231, arXiv:2203.17216, arXiv:2306.16400
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

[[834,32,20]] — one [[4,2,2]] distance-amplification step of [[170,16,10]]

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