Best Known (141−24, 141, s)-Nets in Base 8
(141−24, 141, 43691)-Net over F8 — Constructive and digital
Digital (117, 141, 43691)-net over F8, using
- 81 times duplication [i] based on digital (116, 140, 43691)-net over F8, using
- net defined by OOA [i] based on linear OOA(8140, 43691, F8, 24, 24) (dual of [(43691, 24), 1048444, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(8140, 524292, F8, 24) (dual of [524292, 524152, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8140, 524294, F8, 24) (dual of [524294, 524154, 25]-code), using
- trace code [i] based on linear OA(6470, 262147, F64, 24) (dual of [262147, 262077, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- trace code [i] based on linear OA(6470, 262147, F64, 24) (dual of [262147, 262077, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(8140, 524294, F8, 24) (dual of [524294, 524154, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(8140, 524292, F8, 24) (dual of [524292, 524152, 25]-code), using
- net defined by OOA [i] based on linear OOA(8140, 43691, F8, 24, 24) (dual of [(43691, 24), 1048444, 25]-NRT-code), using
(141−24, 141, 524296)-Net over F8 — Digital
Digital (117, 141, 524296)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8141, 524296, F8, 24) (dual of [524296, 524155, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(8140, 524294, F8, 24) (dual of [524294, 524154, 25]-code), using
- trace code [i] based on linear OA(6470, 262147, F64, 24) (dual of [262147, 262077, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(6470, 262144, F64, 24) (dual of [262144, 262074, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- trace code [i] based on linear OA(6470, 262147, F64, 24) (dual of [262147, 262077, 25]-code), using
- linear OA(8140, 524295, F8, 23) (dual of [524295, 524155, 24]-code), using Gilbert–Varšamov bound and bm = 8140 > Vbs−1(k−1) = 2354 230983 715458 988090 478416 217449 367591 073366 006497 381885 837638 311393 620738 537434 107338 707372 233525 429335 776458 278208 274432 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(8140, 524294, F8, 24) (dual of [524294, 524154, 25]-code), using
- construction X with Varšamov bound [i] based on
(141−24, 141, large)-Net in Base 8 — Upper bound on s
There is no (117, 141, large)-net in base 8, because
- 22 times m-reduction [i] would yield (117, 119, large)-net in base 8, but