Best Known (40, 68, s)-Nets in Base 64
(40, 68, 513)-Net over F64 — Constructive and digital
Digital (40, 68, 513)-net over F64, using
- t-expansion [i] based on digital (28, 68, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(40, 68, 1171)-Net in Base 64 — Constructive
(40, 68, 1171)-net in base 64, using
- net defined by OOA [i] based on OOA(6468, 1171, S64, 28, 28), using
- OA 14-folding and stacking [i] based on OA(6468, 16394, S64, 28), using
- discarding factors based on OA(6468, 16395, S64, 28), using
- discarding parts of the base [i] based on linear OA(12858, 16395, F128, 28) (dual of [16395, 16337, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- construction X applied to Ce(27) ⊂ Ce(23) [i] based on
- discarding parts of the base [i] based on linear OA(12858, 16395, F128, 28) (dual of [16395, 16337, 29]-code), using
- discarding factors based on OA(6468, 16395, S64, 28), using
- OA 14-folding and stacking [i] based on OA(6468, 16394, S64, 28), using
(40, 68, 6151)-Net over F64 — Digital
Digital (40, 68, 6151)-net over F64, using
(40, 68, large)-Net in Base 64 — Upper bound on s
There is no (40, 68, large)-net in base 64, because
- 26 times m-reduction [i] would yield (40, 42, large)-net in base 64, but