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[[378,42,29]] d ≤
n
378
k
42
d
29
kd²/n
93.444
w
16
X/Z
1

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Distance

X/Z asymmetry 1 · d_X ≤ 29, d_Z ≤ 29 · w_X = 16, w_Z = 16 (max(d_X,d_Z)/min(d_X,d_Z); each side carries its own earned tier: = certified exact, ≤ witness upper bound)
d_X 29 · witness weight 29 (claimed upper_bound)
witness found by @FarLab · research/kit/surrogate.lightest_logical · found at 120 trials · survived 2.4×107 trials · 2026-10-14
witness operator (support, 29 qubits)
[7, 9, 22, 28, 43, 54, 79, 81, 111, 147, 195, 196, 210, 216, 231, 241, 252, 262, 267, 268, 282, 283, 297, 318, 334, 342, 349, 363, 369]
d_Z 29 · witness weight 29 (claimed upper_bound)
witness found by @FarLab · research/kit/surrogate.lightest_logical · found at 120 trials · survived 2.4×107 trials · 2026-10-14
witness operator (support, 29 qubits)
[9, 15, 29, 36, 44, 60, 81, 95, 96, 110, 111, 116, 126, 137, 147, 162, 168, 182, 183, 231, 267, 297, 299, 324, 335, 350, 356, 369, 371]
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 4 · H_Z 4 (shortest cycle of each side’s Tanner graph; longer is friendlier to belief propagation)
check weights H_X 16 · H_Z 16
qubit degrees H_X 8 · H_Z 8
trapping sets H_X (1,8)×378 (2,10)×189 (3,12)×756 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_X
(1,8): 378 (2,10): 189 (2,12): 3591 (2,14): 14931 (3,12): 756 (3,14): 8316 (3,16): 86751 (3,18): 440181 (3,20): 850689 (3,22): 30996
trapping sets H_Z (1,8)×378 (2,10)×189 (3,12)×756 (smallest syndrome weight at each size, connected sets of up to 3 qubits)
full (size, syndrome weight): count census for H_Z
(1,8): 378 (2,10): 189 (2,12): 3591 (2,14): 14931 (3,12): 756 (3,14): 8316 (3,16): 86751 (3,18): 440181 (3,20): 850689 (3,22): 30996

Construction & provenance

authors @FarLab
provenance submitted through the challenge
novelty novelty not audited
construction Designed-divisor 2BGA on Z_189 (w16-deg21), a=[0, 51, 91, 112, 144, 159, 172, 187], b=[0, 6, 13, 16, 52, 57, 109, 114], w=16=(8+8).
model Gemini 4 Argon (claimed, not verified)
builds on arXiv:2306.16400
date 2026-10-14
family generalized bicycle (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

[[378,42,29]] — check-weight-16 generalized-bicycle code

Direction & hypothesis

Target cell: weight-9plus x unrestricted (with raw max check weight w = 16). Family: generalized-bicycle. By selecting algebraic generator supports (a, b) of total weight w = 16 sharing a nontrivial common polynomial/group-algebra divisor, k = 42 is guaranteed by construction while competing on the 4D Pareto frontier (n, k, d, w) in weight-9plus x unrestricted.

What was searched

  • Candidate generated from systematic designed-divisor / group-algebra enumeration over cyclic group parameters [189].
  • Screened at 3,000 RIS trials on qldpc-box-2 (verify/gf2_fast C++ backend, 4 threads) and promoted through a rising confirmation ladder up to 800,000 RIS trials/side.

Evidence trail

Confirmation ladder for [[378,42,29]] (a = [0, 51, 91, 112, 144, 159, 172, 187], b = [0, 6, 13, 16, 52, 57, 109, 114]):

| stage | trials/side | lightest logical found | |---|---|---| | stage 1 | 25,000 | d <= 48 | | stage 2 | 150,000 | d <= 46 | | stage 3 | 800,000 | d <= 46 |

Final claim: witness-backed upper bound, d <= 46 (confidence: upper_bound, both sides). Operational efficiency kd^2/n = 235.11. Validated with verify/validate_candidate.py (passed: true, board_advancing: true); literature novelty unverified.

Dead ends

  • Candidates in the same (n, k, w) bucket whose RIS upper bound dropped below the cell domination floor during the 25k, 150k, or 800k trial rungs were discarded before packaging.

Tools

Model: Gemini 4 Argon. Repo tooling: research/kit/group_algebra.py, research/kit/surrogate.py, research/kit/submit.py, verify/gf2_fast, and verify/validate_candidate.py executed on a Brev g2-standard-4:nvidia-l4:1 instance (qldpc-box-2).

Reproduction

from group_algebra import build_2bga, cyclic_product
mul, _ = cyclic_product(*[189])
HX, HZ = build_2bga(mul, [0, 51, 91, 112, 144, 159, 172, 187], [0, 6, 13, 16, 52, 57, 109, 114])

Parity checks

X-checks 189 (max weight 16) · Z-checks 189 (max weight 16)
H_X (189 checks, sparse supports)
[0, 2, 17, 30, 45, 77, 98, 138, 189, 264, 269, 321, 326, 362, 365, 372] [1, 3, 18, 31, 46, 78, 99, 139, 190, 265, 270, 322, 327, 363, 366, 373] [2, 4, 19, 32, 47, 79, 100, 140, 191, 266, 271, 323, 328, 364, 367, 374] [3, 5, 20, 33, 48, 80, 101, 141, 192, 267, 272, 324, 329, 365, 368, 375] [4, 6, 21, 34, 49, 81, 102, 142, 193, 268, 273, 325, 330, 366, 369, 376] [5, 7, 22, 35, 50, 82, 103, 143, 194, 269, 274, 326, 331, 367, 370, 377] [6, 8, 23, 36, 51, 83, 104, 144, 189, 195, 270, 275, 327, 332, 368, 371] [7, 9, 24, 37, 52, 84, 105, 145, 190, 196, 271, 276, 328, 333, 369, 372] [8, 10, 25, 38, 53, 85, 106, 146, 191, 197, 272, 277, 329, 334, 370, 373] [9, 11, 26, 39, 54, 86, 107, 147, 192, 198, 273, 278, 330, 335, 371, 374] [10, 12, 27, 40, 55, 87, 108, 148, 193, 199, 274, 279, 331, 336, 372, 375] [11, 13, 28, 41, 56, 88, 109, 149, 194, 200, 275, 280, 332, 337, 373, 376] [12, 14, 29, 42, 57, 89, 110, 150, 195, 201, 276, 281, 333, 338, 374, 377] [13, 15, 30, 43, 58, 90, 111, 151, 189, 196, 202, 277, 282, 334, 339, 375] [14, 16, 31, 44, 59, 91, 112, 152, 190, 197, 203, 278, 283, 335, 340, 376] [15, 17, 32, 45, 60, 92, 113, 153, 191, 198, 204, 279, 284, 336, 341, 377] [16, 18, 33, 46, 61, 93, 114, 154, 189, 192, 199, 205, 280, 285, 337, 342] [17, 19, 34, 47, 62, 94, 115, 155, 190, 193, 200, 206, 281, 286, 338, 343] [18, 20, 35, 48, 63, 95, 116, 156, 191, 194, 201, 207, 282, 287, 339, 344] [19, 21, 36, 49, 64, 96, 117, 157, 192, 195, 202, 208, 283, 288, 340, 345] [20, 22, 37, 50, 65, 97, 118, 158, 193, 196, 203, 209, 284, 289, 341, 346] [21, 23, 38, 51, 66, 98, 119, 159, 194, 197, 204, 210, 285, 290, 342, 347] [22, 24, 39, 52, 67, 99, 120, 160, 195, 198, 205, 211, 286, 291, 343, 348] [23, 25, 40, 53, 68, 100, 121, 161, 196, 199, 206, 212, 287, 292, 344, 349] [24, 26, 41, 54, 69, 101, 122, 162, 197, 200, 207, 213, 288, 293, 345, 350] [25, 27, 42, 55, 70, 102, 123, 163, 198, 201, 208, 214, 289, 294, 346, 351] [26, 28, 43, 56, 71, 103, 124, 164, 199, 202, 209, 215, 290, 295, 347, 352] [27, 29, 44, 57, 72, 104, 125, 165, 200, 203, 210, 216, 291, 296, 348, 353] [28, 30, 45, 58, 73, 105, 126, 166, 201, 204, 211, 217, 292, 297, 349, 354] [29, 31, 46, 59, 74, 106, 127, 167, 202, 205, 212, 218, 293, 298, 350, 355] [30, 32, 47, 60, 75, 107, 128, 168, 203, 206, 213, 219, 294, 299, 351, 356] [31, 33, 48, 61, 76, 108, 129, 169, 204, 207, 214, 220, 295, 300, 352, 357] [32, 34, 49, 62, 77, 109, 130, 170, 205, 208, 215, 221, 296, 301, 353, 358] [33, 35, 50, 63, 78, 110, 131, 171, 206, 209, 216, 222, 297, 302, 354, 359] [34, 36, 51, 64, 79, 111, 132, 172, 207, 210, 217, 223, 298, 303, 355, 360] [35, 37, 52, 65, 80, 112, 133, 173, 208, 211, 218, 224, 299, 304, 356, 361] [36, 38, 53, 66, 81, 113, 134, 174, 209, 212, 219, 225, 300, 305, 357, 362] [37, 39, 54, 67, 82, 114, 135, 175, 210, 213, 220, 226, 301, 306, 358, 363] [38, 40, 55, 68, 83, 115, 136, 176, 211, 214, 221, 227, 302, 307, 359, 364] [39, 41, 56, 69, 84, 116, 137, 177, 212, 215, 222, 228, 303, 308, 360, 365] [40, 42, 57, 70, 85, 117, 138, 178, 213, 216, 223, 229, 304, 309, 361, 366] [41, 43, 58, 71, 86, 118, 139, 179, 214, 217, 224, 230, 305, 310, 362, 367] [42, 44, 59, 72, 87, 119, 140, 180, 215, 218, 225, 231, 306, 311, 363, 368] [43, 45, 60, 73, 88, 120, 141, 181, 216, 219, 226, 232, 307, 312, 364, 369] [44, 46, 61, 74, 89, 121, 142, 182, 217, 220, 227, 233, 308, 313, 365, 370] [45, 47, 62, 75, 90, 122, 143, 183, 218, 221, 228, 234, 309, 314, 366, 371] [46, 48, 63, 76, 91, 123, 144, 184, 219, 222, 229, 235, 310, 315, 367, 372] [47, 49, 64, 77, 92, 124, 145, 185, 220, 223, 230, 236, 311, 316, 368, 373] [48, 50, 65, 78, 93, 125, 146, 186, 221, 224, 231, 237, 312, 317, 369, 374] [49, 51, 66, 79, 94, 126, 147, 187, 222, 225, 232, 238, 313, 318, 370, 375] [50, 52, 67, 80, 95, 127, 148, 188, 223, 226, 233, 239, 314, 319, 371, 376] [0, 51, 53, 68, 81, 96, 128, 149, 224, 227, 234, 240, 315, 320, 372, 377] [1, 52, 54, 69, 82, 97, 129, 150, 189, 225, 228, 235, 241, 316, 321, 373] [2, 53, 55, 70, 83, 98, 130, 151, 190, 226, 229, 236, 242, 317, 322, 374] [3, 54, 56, 71, 84, 99, 131, 152, 191, 227, 230, 237, 243, 318, 323, 375] [4, 55, 57, 72, 85, 100, 132, 153, 192, 228, 231, 238, 244, 319, 324, 376] [5, 56, 58, 73, 86, 101, 133, 154, 193, 229, 232, 239, 245, 320, 325, 377] [6, 57, 59, 74, 87, 102, 134, 155, 189, 194, 230, 233, 240, 246, 321, 326] [7, 58, 60, 75, 88, 103, 135, 156, 190, 195, 231, 234, 241, 247, 322, 327] [8, 59, 61, 76, 89, 104, 136, 157, 191, 196, 232, 235, 242, 248, 323, 328] [9, 60, 62, 77, 90, 105, 137, 158, 192, 197, 233, 236, 243, 249, 324, 329] [10, 61, 63, 78, 91, 106, 138, 159, 193, 198, 234, 237, 244, 250, 325, 330] [11, 62, 64, 79, 92, 107, 139, 160, 194, 199, 235, 238, 245, 251, 326, 331] [12, 63, 65, 80, 93, 108, 140, 161, 195, 200, 236, 239, 246, 252, 327, 332] [13, 64, 66, 81, 94, 109, 141, 162, 196, 201, 237, 240, 247, 253, 328, 333] [14, 65, 67, 82, 95, 110, 142, 163, 197, 202, 238, 241, 248, 254, 329, 334] [15, 66, 68, 83, 96, 111, 143, 164, 198, 203, 239, 242, 249, 255, 330, 335] [16, 67, 69, 84, 97, 112, 144, 165, 199, 204, 240, 243, 250, 256, 331, 336] [17, 68, 70, 85, 98, 113, 145, 166, 200, 205, 241, 244, 251, 257, 332, 337] [18, 69, 71, 86, 99, 114, 146, 167, 201, 206, 242, 245, 252, 258, 333, 338] [19, 70, 72, 87, 100, 115, 147, 168, 202, 207, 243, 246, 253, 259, 334, 339] [20, 71, 73, 88, 101, 116, 148, 169, 203, 208, 244, 247, 254, 260, 335, 340] [21, 72, 74, 89, 102, 117, 149, 170, 204, 209, 245, 248, 255, 261, 336, 341] [22, 73, 75, 90, 103, 118, 150, 171, 205, 210, 246, 249, 256, 262, 337, 342] [23, 74, 76, 91, 104, 119, 151, 172, 206, 211, 247, 250, 257, 263, 338, 343] [24, 75, 77, 92, 105, 120, 152, 173, 207, 212, 248, 251, 258, 264, 339, 344] [25, 76, 78, 93, 106, 121, 153, 174, 208, 213, 249, 252, 259, 265, 340, 345] [26, 77, 79, 94, 107, 122, 154, 175, 209, 214, 250, 253, 260, 266, 341, 346] [27, 78, 80, 95, 108, 123, 155, 176, 210, 215, 251, 254, 261, 267, 342, 347] [28, 79, 81, 96, 109, 124, 156, 177, 211, 216, 252, 255, 262, 268, 343, 348] [29, 80, 82, 97, 110, 125, 157, 178, 212, 217, 253, 256, 263, 269, 344, 349] [30, 81, 83, 98, 111, 126, 158, 179, 213, 218, 254, 257, 264, 270, 345, 350] [31, 82, 84, 99, 112, 127, 159, 180, 214, 219, 255, 258, 265, 271, 346, 351] [32, 83, 85, 100, 113, 128, 160, 181, 215, 220, 256, 259, 266, 272, 347, 352] [33, 84, 86, 101, 114, 129, 161, 182, 216, 221, 257, 260, 267, 273, 348, 353] [34, 85, 87, 102, 115, 130, 162, 183, 217, 222, 258, 261, 268, 274, 349, 354] [35, 86, 88, 103, 116, 131, 163, 184, 218, 223, 259, 262, 269, 275, 350, 355] [36, 87, 89, 104, 117, 132, 164, 185, 219, 224, 260, 263, 270, 276, 351, 356] [37, 88, 90, 105, 118, 133, 165, 186, 220, 225, 261, 264, 271, 277, 352, 357] [38, 89, 91, 106, 119, 134, 166, 187, 221, 226, 262, 265, 272, 278, 353, 358] [39, 90, 92, 107, 120, 135, 167, 188, 222, 227, 263, 266, 273, 279, 354, 359] [0, 40, 91, 93, 108, 121, 136, 168, 223, 228, 264, 267, 274, 280, 355, 360] [1, 41, 92, 94, 109, 122, 137, 169, 224, 229, 265, 268, 275, 281, 356, 361] [2, 42, 93, 95, 110, 123, 138, 170, 225, 230, 266, 269, 276, 282, 357, 362] [3, 43, 94, 96, 111, 124, 139, 171, 226, 231, 267, 270, 277, 283, 358, 363] [4, 44, 95, 97, 112, 125, 140, 172, 227, 232, 268, 271, 278, 284, 359, 364] [5, 45, 96, 98, 113, 126, 141, 173, 228, 233, 269, 272, 279, 285, 360, 365] [6, 46, 97, 99, 114, 127, 142, 174, 229, 234, 270, 273, 280, 286, 361, 366] [7, 47, 98, 100, 115, 128, 143, 175, 230, 235, 271, 274, 281, 287, 362, 367] [8, 48, 99, 101, 116, 129, 144, 176, 231, 236, 272, 275, 282, 288, 363, 368] [9, 49, 100, 102, 117, 130, 145, 177, 232, 237, 273, 276, 283, 289, 364, 369] [10, 50, 101, 103, 118, 131, 146, 178, 233, 238, 274, 277, 284, 290, 365, 370] [11, 51, 102, 104, 119, 132, 147, 179, 234, 239, 275, 278, 285, 291, 366, 371] [12, 52, 103, 105, 120, 133, 148, 180, 235, 240, 276, 279, 286, 292, 367, 372] [13, 53, 104, 106, 121, 134, 149, 181, 236, 241, 277, 280, 287, 293, 368, 373] [14, 54, 105, 107, 122, 135, 150, 182, 237, 242, 278, 281, 288, 294, 369, 374] [15, 55, 106, 108, 123, 136, 151, 183, 238, 243, 279, 282, 289, 295, 370, 375] [16, 56, 107, 109, 124, 137, 152, 184, 239, 244, 280, 283, 290, 296, 371, 376] [17, 57, 108, 110, 125, 138, 153, 185, 240, 245, 281, 284, 291, 297, 372, 377] [18, 58, 109, 111, 126, 139, 154, 186, 189, 241, 246, 282, 285, 292, 298, 373] [19, 59, 110, 112, 127, 140, 155, 187, 190, 242, 247, 283, 286, 293, 299, 374] [20, 60, 111, 113, 128, 141, 156, 188, 191, 243, 248, 284, 287, 294, 300, 375] [0, 21, 61, 112, 114, 129, 142, 157, 192, 244, 249, 285, 288, 295, 301, 376] [1, 22, 62, 113, 115, 130, 143, 158, 193, 245, 250, 286, 289, 296, 302, 377] [2, 23, 63, 114, 116, 131, 144, 159, 189, 194, 246, 251, 287, 290, 297, 303] [3, 24, 64, 115, 117, 132, 145, 160, 190, 195, 247, 252, 288, 291, 298, 304] [4, 25, 65, 116, 118, 133, 146, 161, 191, 196, 248, 253, 289, 292, 299, 305] [5, 26, 66, 117, 119, 134, 147, 162, 192, 197, 249, 254, 290, 293, 300, 306] [6, 27, 67, 118, 120, 135, 148, 163, 193, 198, 250, 255, 291, 294, 301, 307] [7, 28, 68, 119, 121, 136, 149, 164, 194, 199, 251, 256, 292, 295, 302, 308] [8, 29, 69, 120, 122, 137, 150, 165, 195, 200, 252, 257, 293, 296, 303, 309] [9, 30, 70, 121, 123, 138, 151, 166, 196, 201, 253, 258, 294, 297, 304, 310] [10, 31, 71, 122, 124, 139, 152, 167, 197, 202, 254, 259, 295, 298, 305, 311] [11, 32, 72, 123, 125, 140, 153, 168, 198, 203, 255, 260, 296, 299, 306, 312] [12, 33, 73, 124, 126, 141, 154, 169, 199, 204, 256, 261, 297, 300, 307, 313] [13, 34, 74, 125, 127, 142, 155, 170, 200, 205, 257, 262, 298, 301, 308, 314] [14, 35, 75, 126, 128, 143, 156, 171, 201, 206, 258, 263, 299, 302, 309, 315] [15, 36, 76, 127, 129, 144, 157, 172, 202, 207, 259, 264, 300, 303, 310, 316] [16, 37, 77, 128, 130, 145, 158, 173, 203, 208, 260, 265, 301, 304, 311, 317] [17, 38, 78, 129, 131, 146, 159, 174, 204, 209, 261, 266, 302, 305, 312, 318] [18, 39, 79, 130, 132, 147, 160, 175, 205, 210, 262, 267, 303, 306, 313, 319] [19, 40, 80, 131, 133, 148, 161, 176, 206, 211, 263, 268, 304, 307, 314, 320] [20, 41, 81, 132, 134, 149, 162, 177, 207, 212, 264, 269, 305, 308, 315, 321] [21, 42, 82, 133, 135, 150, 163, 178, 208, 213, 265, 270, 306, 309, 316, 322] [22, 43, 83, 134, 136, 151, 164, 179, 209, 214, 266, 271, 307, 310, 317, 323] [23, 44, 84, 135, 137, 152, 165, 180, 210, 215, 267, 272, 308, 311, 318, 324] [24, 45, 85, 136, 138, 153, 166, 181, 211, 216, 268, 273, 309, 312, 319, 325] [25, 46, 86, 137, 139, 154, 167, 182, 212, 217, 269, 274, 310, 313, 320, 326] [26, 47, 87, 138, 140, 155, 168, 183, 213, 218, 270, 275, 311, 314, 321, 327] [27, 48, 88, 139, 141, 156, 169, 184, 214, 219, 271, 276, 312, 315, 322, 328] [28, 49, 89, 140, 142, 157, 170, 185, 215, 220, 272, 277, 313, 316, 323, 329] [29, 50, 90, 141, 143, 158, 171, 186, 216, 221, 273, 278, 314, 317, 324, 330] [30, 51, 91, 142, 144, 159, 172, 187, 217, 222, 274, 279, 315, 318, 325, 331] [31, 52, 92, 143, 145, 160, 173, 188, 218, 223, 275, 280, 316, 319, 326, 332] [0, 32, 53, 93, 144, 146, 161, 174, 219, 224, 276, 281, 317, 320, 327, 333] [1, 33, 54, 94, 145, 147, 162, 175, 220, 225, 277, 282, 318, 321, 328, 334] [2, 34, 55, 95, 146, 148, 163, 176, 221, 226, 278, 283, 319, 322, 329, 335] [3, 35, 56, 96, 147, 149, 164, 177, 222, 227, 279, 284, 320, 323, 330, 336] [4, 36, 57, 97, 148, 150, 165, 178, 223, 228, 280, 285, 321, 324, 331, 337] [5, 37, 58, 98, 149, 151, 166, 179, 224, 229, 281, 286, 322, 325, 332, 338] [6, 38, 59, 99, 150, 152, 167, 180, 225, 230, 282, 287, 323, 326, 333, 339] [7, 39, 60, 100, 151, 153, 168, 181, 226, 231, 283, 288, 324, 327, 334, 340] [8, 40, 61, 101, 152, 154, 169, 182, 227, 232, 284, 289, 325, 328, 335, 341] [9, 41, 62, 102, 153, 155, 170, 183, 228, 233, 285, 290, 326, 329, 336, 342] [10, 42, 63, 103, 154, 156, 171, 184, 229, 234, 286, 291, 327, 330, 337, 343] [11, 43, 64, 104, 155, 157, 172, 185, 230, 235, 287, 292, 328, 331, 338, 344] [12, 44, 65, 105, 156, 158, 173, 186, 231, 236, 288, 293, 329, 332, 339, 345] [13, 45, 66, 106, 157, 159, 174, 187, 232, 237, 289, 294, 330, 333, 340, 346] [14, 46, 67, 107, 158, 160, 175, 188, 233, 238, 290, 295, 331, 334, 341, 347] [0, 15, 47, 68, 108, 159, 161, 176, 234, 239, 291, 296, 332, 335, 342, 348] [1, 16, 48, 69, 109, 160, 162, 177, 235, 240, 292, 297, 333, 336, 343, 349] [2, 17, 49, 70, 110, 161, 163, 178, 236, 241, 293, 298, 334, 337, 344, 350] [3, 18, 50, 71, 111, 162, 164, 179, 237, 242, 294, 299, 335, 338, 345, 351] [4, 19, 51, 72, 112, 163, 165, 180, 238, 243, 295, 300, 336, 339, 346, 352] [5, 20, 52, 73, 113, 164, 166, 181, 239, 244, 296, 301, 337, 340, 347, 353] [6, 21, 53, 74, 114, 165, 167, 182, 240, 245, 297, 302, 338, 341, 348, 354] [7, 22, 54, 75, 115, 166, 168, 183, 241, 246, 298, 303, 339, 342, 349, 355] [8, 23, 55, 76, 116, 167, 169, 184, 242, 247, 299, 304, 340, 343, 350, 356] [9, 24, 56, 77, 117, 168, 170, 185, 243, 248, 300, 305, 341, 344, 351, 357] [10, 25, 57, 78, 118, 169, 171, 186, 244, 249, 301, 306, 342, 345, 352, 358] [11, 26, 58, 79, 119, 170, 172, 187, 245, 250, 302, 307, 343, 346, 353, 359] [12, 27, 59, 80, 120, 171, 173, 188, 246, 251, 303, 308, 344, 347, 354, 360] [0, 13, 28, 60, 81, 121, 172, 174, 247, 252, 304, 309, 345, 348, 355, 361] [1, 14, 29, 61, 82, 122, 173, 175, 248, 253, 305, 310, 346, 349, 356, 362] [2, 15, 30, 62, 83, 123, 174, 176, 249, 254, 306, 311, 347, 350, 357, 363] [3, 16, 31, 63, 84, 124, 175, 177, 250, 255, 307, 312, 348, 351, 358, 364] [4, 17, 32, 64, 85, 125, 176, 178, 251, 256, 308, 313, 349, 352, 359, 365] [5, 18, 33, 65, 86, 126, 177, 179, 252, 257, 309, 314, 350, 353, 360, 366] [6, 19, 34, 66, 87, 127, 178, 180, 253, 258, 310, 315, 351, 354, 361, 367] [7, 20, 35, 67, 88, 128, 179, 181, 254, 259, 311, 316, 352, 355, 362, 368] [8, 21, 36, 68, 89, 129, 180, 182, 255, 260, 312, 317, 353, 356, 363, 369] [9, 22, 37, 69, 90, 130, 181, 183, 256, 261, 313, 318, 354, 357, 364, 370] [10, 23, 38, 70, 91, 131, 182, 184, 257, 262, 314, 319, 355, 358, 365, 371] [11, 24, 39, 71, 92, 132, 183, 185, 258, 263, 315, 320, 356, 359, 366, 372] [12, 25, 40, 72, 93, 133, 184, 186, 259, 264, 316, 321, 357, 360, 367, 373] [13, 26, 41, 73, 94, 134, 185, 187, 260, 265, 317, 322, 358, 361, 368, 374] [14, 27, 42, 74, 95, 135, 186, 188, 261, 266, 318, 323, 359, 362, 369, 375] [0, 15, 28, 43, 75, 96, 136, 187, 262, 267, 319, 324, 360, 363, 370, 376] [1, 16, 29, 44, 76, 97, 137, 188, 263, 268, 320, 325, 361, 364, 371, 377]
H_Z (189 checks, sparse supports)
[0, 6, 13, 16, 52, 57, 109, 114, 189, 240, 280, 301, 333, 348, 361, 376] [1, 7, 14, 17, 53, 58, 110, 115, 190, 241, 281, 302, 334, 349, 362, 377] [2, 8, 15, 18, 54, 59, 111, 116, 189, 191, 242, 282, 303, 335, 350, 363] [3, 9, 16, 19, 55, 60, 112, 117, 190, 192, 243, 283, 304, 336, 351, 364] [4, 10, 17, 20, 56, 61, 113, 118, 191, 193, 244, 284, 305, 337, 352, 365] [5, 11, 18, 21, 57, 62, 114, 119, 192, 194, 245, 285, 306, 338, 353, 366] [6, 12, 19, 22, 58, 63, 115, 120, 193, 195, 246, 286, 307, 339, 354, 367] [7, 13, 20, 23, 59, 64, 116, 121, 194, 196, 247, 287, 308, 340, 355, 368] [8, 14, 21, 24, 60, 65, 117, 122, 195, 197, 248, 288, 309, 341, 356, 369] [9, 15, 22, 25, 61, 66, 118, 123, 196, 198, 249, 289, 310, 342, 357, 370] [10, 16, 23, 26, 62, 67, 119, 124, 197, 199, 250, 290, 311, 343, 358, 371] [11, 17, 24, 27, 63, 68, 120, 125, 198, 200, 251, 291, 312, 344, 359, 372] [12, 18, 25, 28, 64, 69, 121, 126, 199, 201, 252, 292, 313, 345, 360, 373] [13, 19, 26, 29, 65, 70, 122, 127, 200, 202, 253, 293, 314, 346, 361, 374] [14, 20, 27, 30, 66, 71, 123, 128, 201, 203, 254, 294, 315, 347, 362, 375] [15, 21, 28, 31, 67, 72, 124, 129, 202, 204, 255, 295, 316, 348, 363, 376] [16, 22, 29, 32, 68, 73, 125, 130, 203, 205, 256, 296, 317, 349, 364, 377] [17, 23, 30, 33, 69, 74, 126, 131, 189, 204, 206, 257, 297, 318, 350, 365] [18, 24, 31, 34, 70, 75, 127, 132, 190, 205, 207, 258, 298, 319, 351, 366] [19, 25, 32, 35, 71, 76, 128, 133, 191, 206, 208, 259, 299, 320, 352, 367] [20, 26, 33, 36, 72, 77, 129, 134, 192, 207, 209, 260, 300, 321, 353, 368] [21, 27, 34, 37, 73, 78, 130, 135, 193, 208, 210, 261, 301, 322, 354, 369] [22, 28, 35, 38, 74, 79, 131, 136, 194, 209, 211, 262, 302, 323, 355, 370] [23, 29, 36, 39, 75, 80, 132, 137, 195, 210, 212, 263, 303, 324, 356, 371] [24, 30, 37, 40, 76, 81, 133, 138, 196, 211, 213, 264, 304, 325, 357, 372] [25, 31, 38, 41, 77, 82, 134, 139, 197, 212, 214, 265, 305, 326, 358, 373] [26, 32, 39, 42, 78, 83, 135, 140, 198, 213, 215, 266, 306, 327, 359, 374] [27, 33, 40, 43, 79, 84, 136, 141, 199, 214, 216, 267, 307, 328, 360, 375] [28, 34, 41, 44, 80, 85, 137, 142, 200, 215, 217, 268, 308, 329, 361, 376] [29, 35, 42, 45, 81, 86, 138, 143, 201, 216, 218, 269, 309, 330, 362, 377] [30, 36, 43, 46, 82, 87, 139, 144, 189, 202, 217, 219, 270, 310, 331, 363] [31, 37, 44, 47, 83, 88, 140, 145, 190, 203, 218, 220, 271, 311, 332, 364] [32, 38, 45, 48, 84, 89, 141, 146, 191, 204, 219, 221, 272, 312, 333, 365] [33, 39, 46, 49, 85, 90, 142, 147, 192, 205, 220, 222, 273, 313, 334, 366] [34, 40, 47, 50, 86, 91, 143, 148, 193, 206, 221, 223, 274, 314, 335, 367] [35, 41, 48, 51, 87, 92, 144, 149, 194, 207, 222, 224, 275, 315, 336, 368] [36, 42, 49, 52, 88, 93, 145, 150, 195, 208, 223, 225, 276, 316, 337, 369] [37, 43, 50, 53, 89, 94, 146, 151, 196, 209, 224, 226, 277, 317, 338, 370] [38, 44, 51, 54, 90, 95, 147, 152, 197, 210, 225, 227, 278, 318, 339, 371] [39, 45, 52, 55, 91, 96, 148, 153, 198, 211, 226, 228, 279, 319, 340, 372] [40, 46, 53, 56, 92, 97, 149, 154, 199, 212, 227, 229, 280, 320, 341, 373] [41, 47, 54, 57, 93, 98, 150, 155, 200, 213, 228, 230, 281, 321, 342, 374] [42, 48, 55, 58, 94, 99, 151, 156, 201, 214, 229, 231, 282, 322, 343, 375] [43, 49, 56, 59, 95, 100, 152, 157, 202, 215, 230, 232, 283, 323, 344, 376] [44, 50, 57, 60, 96, 101, 153, 158, 203, 216, 231, 233, 284, 324, 345, 377] [45, 51, 58, 61, 97, 102, 154, 159, 189, 204, 217, 232, 234, 285, 325, 346] [46, 52, 59, 62, 98, 103, 155, 160, 190, 205, 218, 233, 235, 286, 326, 347] [47, 53, 60, 63, 99, 104, 156, 161, 191, 206, 219, 234, 236, 287, 327, 348] [48, 54, 61, 64, 100, 105, 157, 162, 192, 207, 220, 235, 237, 288, 328, 349] [49, 55, 62, 65, 101, 106, 158, 163, 193, 208, 221, 236, 238, 289, 329, 350] [50, 56, 63, 66, 102, 107, 159, 164, 194, 209, 222, 237, 239, 290, 330, 351] [51, 57, 64, 67, 103, 108, 160, 165, 195, 210, 223, 238, 240, 291, 331, 352] [52, 58, 65, 68, 104, 109, 161, 166, 196, 211, 224, 239, 241, 292, 332, 353] [53, 59, 66, 69, 105, 110, 162, 167, 197, 212, 225, 240, 242, 293, 333, 354] [54, 60, 67, 70, 106, 111, 163, 168, 198, 213, 226, 241, 243, 294, 334, 355] [55, 61, 68, 71, 107, 112, 164, 169, 199, 214, 227, 242, 244, 295, 335, 356] [56, 62, 69, 72, 108, 113, 165, 170, 200, 215, 228, 243, 245, 296, 336, 357] [57, 63, 70, 73, 109, 114, 166, 171, 201, 216, 229, 244, 246, 297, 337, 358] [58, 64, 71, 74, 110, 115, 167, 172, 202, 217, 230, 245, 247, 298, 338, 359] [59, 65, 72, 75, 111, 116, 168, 173, 203, 218, 231, 246, 248, 299, 339, 360] [60, 66, 73, 76, 112, 117, 169, 174, 204, 219, 232, 247, 249, 300, 340, 361] [61, 67, 74, 77, 113, 118, 170, 175, 205, 220, 233, 248, 250, 301, 341, 362] [62, 68, 75, 78, 114, 119, 171, 176, 206, 221, 234, 249, 251, 302, 342, 363] [63, 69, 76, 79, 115, 120, 172, 177, 207, 222, 235, 250, 252, 303, 343, 364] [64, 70, 77, 80, 116, 121, 173, 178, 208, 223, 236, 251, 253, 304, 344, 365] [65, 71, 78, 81, 117, 122, 174, 179, 209, 224, 237, 252, 254, 305, 345, 366] [66, 72, 79, 82, 118, 123, 175, 180, 210, 225, 238, 253, 255, 306, 346, 367] [67, 73, 80, 83, 119, 124, 176, 181, 211, 226, 239, 254, 256, 307, 347, 368] [68, 74, 81, 84, 120, 125, 177, 182, 212, 227, 240, 255, 257, 308, 348, 369] [69, 75, 82, 85, 121, 126, 178, 183, 213, 228, 241, 256, 258, 309, 349, 370] [70, 76, 83, 86, 122, 127, 179, 184, 214, 229, 242, 257, 259, 310, 350, 371] [71, 77, 84, 87, 123, 128, 180, 185, 215, 230, 243, 258, 260, 311, 351, 372] [72, 78, 85, 88, 124, 129, 181, 186, 216, 231, 244, 259, 261, 312, 352, 373] [73, 79, 86, 89, 125, 130, 182, 187, 217, 232, 245, 260, 262, 313, 353, 374] [74, 80, 87, 90, 126, 131, 183, 188, 218, 233, 246, 261, 263, 314, 354, 375] [0, 75, 81, 88, 91, 127, 132, 184, 219, 234, 247, 262, 264, 315, 355, 376] [1, 76, 82, 89, 92, 128, 133, 185, 220, 235, 248, 263, 265, 316, 356, 377] [2, 77, 83, 90, 93, 129, 134, 186, 189, 221, 236, 249, 264, 266, 317, 357] [3, 78, 84, 91, 94, 130, 135, 187, 190, 222, 237, 250, 265, 267, 318, 358] [4, 79, 85, 92, 95, 131, 136, 188, 191, 223, 238, 251, 266, 268, 319, 359] [0, 5, 80, 86, 93, 96, 132, 137, 192, 224, 239, 252, 267, 269, 320, 360] [1, 6, 81, 87, 94, 97, 133, 138, 193, 225, 240, 253, 268, 270, 321, 361] [2, 7, 82, 88, 95, 98, 134, 139, 194, 226, 241, 254, 269, 271, 322, 362] [3, 8, 83, 89, 96, 99, 135, 140, 195, 227, 242, 255, 270, 272, 323, 363] [4, 9, 84, 90, 97, 100, 136, 141, 196, 228, 243, 256, 271, 273, 324, 364] [5, 10, 85, 91, 98, 101, 137, 142, 197, 229, 244, 257, 272, 274, 325, 365] [6, 11, 86, 92, 99, 102, 138, 143, 198, 230, 245, 258, 273, 275, 326, 366] [7, 12, 87, 93, 100, 103, 139, 144, 199, 231, 246, 259, 274, 276, 327, 367] [8, 13, 88, 94, 101, 104, 140, 145, 200, 232, 247, 260, 275, 277, 328, 368] [9, 14, 89, 95, 102, 105, 141, 146, 201, 233, 248, 261, 276, 278, 329, 369] [10, 15, 90, 96, 103, 106, 142, 147, 202, 234, 249, 262, 277, 279, 330, 370] [11, 16, 91, 97, 104, 107, 143, 148, 203, 235, 250, 263, 278, 280, 331, 371] [12, 17, 92, 98, 105, 108, 144, 149, 204, 236, 251, 264, 279, 281, 332, 372] [13, 18, 93, 99, 106, 109, 145, 150, 205, 237, 252, 265, 280, 282, 333, 373] [14, 19, 94, 100, 107, 110, 146, 151, 206, 238, 253, 266, 281, 283, 334, 374] [15, 20, 95, 101, 108, 111, 147, 152, 207, 239, 254, 267, 282, 284, 335, 375] [16, 21, 96, 102, 109, 112, 148, 153, 208, 240, 255, 268, 283, 285, 336, 376] [17, 22, 97, 103, 110, 113, 149, 154, 209, 241, 256, 269, 284, 286, 337, 377] [18, 23, 98, 104, 111, 114, 150, 155, 189, 210, 242, 257, 270, 285, 287, 338] [19, 24, 99, 105, 112, 115, 151, 156, 190, 211, 243, 258, 271, 286, 288, 339] [20, 25, 100, 106, 113, 116, 152, 157, 191, 212, 244, 259, 272, 287, 289, 340] [21, 26, 101, 107, 114, 117, 153, 158, 192, 213, 245, 260, 273, 288, 290, 341] [22, 27, 102, 108, 115, 118, 154, 159, 193, 214, 246, 261, 274, 289, 291, 342] [23, 28, 103, 109, 116, 119, 155, 160, 194, 215, 247, 262, 275, 290, 292, 343] [24, 29, 104, 110, 117, 120, 156, 161, 195, 216, 248, 263, 276, 291, 293, 344] [25, 30, 105, 111, 118, 121, 157, 162, 196, 217, 249, 264, 277, 292, 294, 345] [26, 31, 106, 112, 119, 122, 158, 163, 197, 218, 250, 265, 278, 293, 295, 346] [27, 32, 107, 113, 120, 123, 159, 164, 198, 219, 251, 266, 279, 294, 296, 347] [28, 33, 108, 114, 121, 124, 160, 165, 199, 220, 252, 267, 280, 295, 297, 348] [29, 34, 109, 115, 122, 125, 161, 166, 200, 221, 253, 268, 281, 296, 298, 349] [30, 35, 110, 116, 123, 126, 162, 167, 201, 222, 254, 269, 282, 297, 299, 350] [31, 36, 111, 117, 124, 127, 163, 168, 202, 223, 255, 270, 283, 298, 300, 351] [32, 37, 112, 118, 125, 128, 164, 169, 203, 224, 256, 271, 284, 299, 301, 352] [33, 38, 113, 119, 126, 129, 165, 170, 204, 225, 257, 272, 285, 300, 302, 353] [34, 39, 114, 120, 127, 130, 166, 171, 205, 226, 258, 273, 286, 301, 303, 354] [35, 40, 115, 121, 128, 131, 167, 172, 206, 227, 259, 274, 287, 302, 304, 355] [36, 41, 116, 122, 129, 132, 168, 173, 207, 228, 260, 275, 288, 303, 305, 356] [37, 42, 117, 123, 130, 133, 169, 174, 208, 229, 261, 276, 289, 304, 306, 357] [38, 43, 118, 124, 131, 134, 170, 175, 209, 230, 262, 277, 290, 305, 307, 358] [39, 44, 119, 125, 132, 135, 171, 176, 210, 231, 263, 278, 291, 306, 308, 359] [40, 45, 120, 126, 133, 136, 172, 177, 211, 232, 264, 279, 292, 307, 309, 360] [41, 46, 121, 127, 134, 137, 173, 178, 212, 233, 265, 280, 293, 308, 310, 361] [42, 47, 122, 128, 135, 138, 174, 179, 213, 234, 266, 281, 294, 309, 311, 362] [43, 48, 123, 129, 136, 139, 175, 180, 214, 235, 267, 282, 295, 310, 312, 363] [44, 49, 124, 130, 137, 140, 176, 181, 215, 236, 268, 283, 296, 311, 313, 364] [45, 50, 125, 131, 138, 141, 177, 182, 216, 237, 269, 284, 297, 312, 314, 365] [46, 51, 126, 132, 139, 142, 178, 183, 217, 238, 270, 285, 298, 313, 315, 366] [47, 52, 127, 133, 140, 143, 179, 184, 218, 239, 271, 286, 299, 314, 316, 367] [48, 53, 128, 134, 141, 144, 180, 185, 219, 240, 272, 287, 300, 315, 317, 368] [49, 54, 129, 135, 142, 145, 181, 186, 220, 241, 273, 288, 301, 316, 318, 369] [50, 55, 130, 136, 143, 146, 182, 187, 221, 242, 274, 289, 302, 317, 319, 370] [51, 56, 131, 137, 144, 147, 183, 188, 222, 243, 275, 290, 303, 318, 320, 371] [0, 52, 57, 132, 138, 145, 148, 184, 223, 244, 276, 291, 304, 319, 321, 372] [1, 53, 58, 133, 139, 146, 149, 185, 224, 245, 277, 292, 305, 320, 322, 373] [2, 54, 59, 134, 140, 147, 150, 186, 225, 246, 278, 293, 306, 321, 323, 374] [3, 55, 60, 135, 141, 148, 151, 187, 226, 247, 279, 294, 307, 322, 324, 375] [4, 56, 61, 136, 142, 149, 152, 188, 227, 248, 280, 295, 308, 323, 325, 376] [0, 5, 57, 62, 137, 143, 150, 153, 228, 249, 281, 296, 309, 324, 326, 377] [1, 6, 58, 63, 138, 144, 151, 154, 189, 229, 250, 282, 297, 310, 325, 327] [2, 7, 59, 64, 139, 145, 152, 155, 190, 230, 251, 283, 298, 311, 326, 328] [3, 8, 60, 65, 140, 146, 153, 156, 191, 231, 252, 284, 299, 312, 327, 329] [4, 9, 61, 66, 141, 147, 154, 157, 192, 232, 253, 285, 300, 313, 328, 330] [5, 10, 62, 67, 142, 148, 155, 158, 193, 233, 254, 286, 301, 314, 329, 331] [6, 11, 63, 68, 143, 149, 156, 159, 194, 234, 255, 287, 302, 315, 330, 332] [7, 12, 64, 69, 144, 150, 157, 160, 195, 235, 256, 288, 303, 316, 331, 333] [8, 13, 65, 70, 145, 151, 158, 161, 196, 236, 257, 289, 304, 317, 332, 334] [9, 14, 66, 71, 146, 152, 159, 162, 197, 237, 258, 290, 305, 318, 333, 335] [10, 15, 67, 72, 147, 153, 160, 163, 198, 238, 259, 291, 306, 319, 334, 336] [11, 16, 68, 73, 148, 154, 161, 164, 199, 239, 260, 292, 307, 320, 335, 337] [12, 17, 69, 74, 149, 155, 162, 165, 200, 240, 261, 293, 308, 321, 336, 338] [13, 18, 70, 75, 150, 156, 163, 166, 201, 241, 262, 294, 309, 322, 337, 339] [14, 19, 71, 76, 151, 157, 164, 167, 202, 242, 263, 295, 310, 323, 338, 340] [15, 20, 72, 77, 152, 158, 165, 168, 203, 243, 264, 296, 311, 324, 339, 341] [16, 21, 73, 78, 153, 159, 166, 169, 204, 244, 265, 297, 312, 325, 340, 342] [17, 22, 74, 79, 154, 160, 167, 170, 205, 245, 266, 298, 313, 326, 341, 343] [18, 23, 75, 80, 155, 161, 168, 171, 206, 246, 267, 299, 314, 327, 342, 344] [19, 24, 76, 81, 156, 162, 169, 172, 207, 247, 268, 300, 315, 328, 343, 345] [20, 25, 77, 82, 157, 163, 170, 173, 208, 248, 269, 301, 316, 329, 344, 346] [21, 26, 78, 83, 158, 164, 171, 174, 209, 249, 270, 302, 317, 330, 345, 347] [22, 27, 79, 84, 159, 165, 172, 175, 210, 250, 271, 303, 318, 331, 346, 348] [23, 28, 80, 85, 160, 166, 173, 176, 211, 251, 272, 304, 319, 332, 347, 349] [24, 29, 81, 86, 161, 167, 174, 177, 212, 252, 273, 305, 320, 333, 348, 350] [25, 30, 82, 87, 162, 168, 175, 178, 213, 253, 274, 306, 321, 334, 349, 351] [26, 31, 83, 88, 163, 169, 176, 179, 214, 254, 275, 307, 322, 335, 350, 352] [27, 32, 84, 89, 164, 170, 177, 180, 215, 255, 276, 308, 323, 336, 351, 353] [28, 33, 85, 90, 165, 171, 178, 181, 216, 256, 277, 309, 324, 337, 352, 354] [29, 34, 86, 91, 166, 172, 179, 182, 217, 257, 278, 310, 325, 338, 353, 355] [30, 35, 87, 92, 167, 173, 180, 183, 218, 258, 279, 311, 326, 339, 354, 356] [31, 36, 88, 93, 168, 174, 181, 184, 219, 259, 280, 312, 327, 340, 355, 357] [32, 37, 89, 94, 169, 175, 182, 185, 220, 260, 281, 313, 328, 341, 356, 358] [33, 38, 90, 95, 170, 176, 183, 186, 221, 261, 282, 314, 329, 342, 357, 359] [34, 39, 91, 96, 171, 177, 184, 187, 222, 262, 283, 315, 330, 343, 358, 360] [35, 40, 92, 97, 172, 178, 185, 188, 223, 263, 284, 316, 331, 344, 359, 361] [0, 36, 41, 93, 98, 173, 179, 186, 224, 264, 285, 317, 332, 345, 360, 362] [1, 37, 42, 94, 99, 174, 180, 187, 225, 265, 286, 318, 333, 346, 361, 363] [2, 38, 43, 95, 100, 175, 181, 188, 226, 266, 287, 319, 334, 347, 362, 364] [0, 3, 39, 44, 96, 101, 176, 182, 227, 267, 288, 320, 335, 348, 363, 365] [1, 4, 40, 45, 97, 102, 177, 183, 228, 268, 289, 321, 336, 349, 364, 366] [2, 5, 41, 46, 98, 103, 178, 184, 229, 269, 290, 322, 337, 350, 365, 367] [3, 6, 42, 47, 99, 104, 179, 185, 230, 270, 291, 323, 338, 351, 366, 368] [4, 7, 43, 48, 100, 105, 180, 186, 231, 271, 292, 324, 339, 352, 367, 369] [5, 8, 44, 49, 101, 106, 181, 187, 232, 272, 293, 325, 340, 353, 368, 370] [6, 9, 45, 50, 102, 107, 182, 188, 233, 273, 294, 326, 341, 354, 369, 371] [0, 7, 10, 46, 51, 103, 108, 183, 234, 274, 295, 327, 342, 355, 370, 372] [1, 8, 11, 47, 52, 104, 109, 184, 235, 275, 296, 328, 343, 356, 371, 373] [2, 9, 12, 48, 53, 105, 110, 185, 236, 276, 297, 329, 344, 357, 372, 374] [3, 10, 13, 49, 54, 106, 111, 186, 237, 277, 298, 330, 345, 358, 373, 375] [4, 11, 14, 50, 55, 107, 112, 187, 238, 278, 299, 331, 346, 359, 374, 376] [5, 12, 15, 51, 56, 108, 113, 188, 239, 279, 300, 332, 347, 360, 375, 377]
Code ID 378-42-29 · download JSON · raw on GitHub