← back to the board
[[336,6,14]] d ≤
n
336
k
6
d
14
kd²/n
3.5
w
6
g
0.0121
r
4.1231
layers
2

Share this result

Distance

d_X 14 · witness weight 14 (claimed upper_bound)
witness operator (support, 14 qubits)
[20, 36, 49, 78, 118, 119, 176, 191, 260, 272, 273, 287, 301, 328]
d_Z 14 · witness weight 14 (claimed upper_bound)
witness operator (support, 14 qubits)
[1, 3, 5, 7, 9, 11, 13, 169, 171, 173, 175, 177, 179, 181]
certificate none yet · distance stands as a self-certified upper bound (d ≤)

Verified 2D layout

as measured by the verifier: every check drawn over the submitted coordinates; the interaction radius is the longest dashed pair
r = 4.123
X checkZ checkqubit site (168)2 qubits stacked (2 layers)dashed: the pair setting the interaction radiushover a check to isolate its qubits; click to pin — repeated clicks cycle through overlapping checks; click empty space to release

Construction & provenance

authors @FarLab and @vprusso
provenance submitted through the challenge
novelty novelty not audited
construction f = 1 + xy + x-1 y2, g = 1 + x-1 y + x-2 y-1; annulus-type boundary engine, (12,14) lattice.
model Claude Claude Opus 4.8 (claimed, not verified)
builds on arXiv:2504.08887
date 2026-06-16
family bivariate bicycle (a tag, not a ranking)
locality 2D-local bilayer (computed from the layout)
weight class weight ≤ 6 (computed)

How this code was found

no research note was staged with this submission — notes are requested for new submissions (notes/README.md)

Parity checks

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