Best Known (38, 38+32, s)-Nets in Base 64
(38, 38+32, 513)-Net over F64 — Constructive and digital
Digital (38, 70, 513)-net over F64, using
- t-expansion [i] based on digital (28, 70, 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
(38, 38+32, 545)-Net in Base 64 — Constructive
(38, 70, 545)-net in base 64, using
- (u, u+v)-construction [i] based on
- (6, 22, 257)-net in base 64, using
- 2 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- base change [i] based on digital (0, 18, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 18, 257)-net over F256, using
- 2 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- (16, 48, 288)-net in base 64, using
- 1 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 42, 288)-net over F128, using
- 1 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- (6, 22, 257)-net in base 64, using
(38, 38+32, 2713)-Net over F64 — Digital
Digital (38, 70, 2713)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6470, 2713, F64, 32) (dual of [2713, 2643, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(6470, 4119, F64, 32) (dual of [4119, 4049, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(23) [i] based on
- linear OA(6463, 4096, F64, 32) (dual of [4096, 4033, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(6447, 4096, F64, 24) (dual of [4096, 4049, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(647, 23, F64, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- construction X applied to Ce(31) ⊂ Ce(23) [i] based on
- discarding factors / shortening the dual code based on linear OA(6470, 4119, F64, 32) (dual of [4119, 4049, 33]-code), using
(38, 38+32, large)-Net in Base 64 — Upper bound on s
There is no (38, 70, large)-net in base 64, because
- 30 times m-reduction [i] would yield (38, 40, large)-net in base 64, but