Best Known (47, 87, s)-Nets in Base 64
(47, 87, 513)-Net over F64 — Constructive and digital
Digital (47, 87, 513)-net over F64, using
- t-expansion [i] based on digital (28, 87, 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
(47, 87, 546)-Net in Base 64 — Constructive
(47, 87, 546)-net in base 64, using
- t-expansion [i] based on (46, 87, 546)-net in base 64, using
- (u, u+v)-construction [i] based on
- (8, 28, 258)-net in base 64, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- (18, 59, 288)-net in base 64, using
- 4 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 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, 54, 288)-net over F128, using
- 4 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- (8, 28, 258)-net in base 64, using
- (u, u+v)-construction [i] based on
(47, 87, 2900)-Net over F64 — Digital
Digital (47, 87, 2900)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6487, 2900, F64, 40) (dual of [2900, 2813, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(6487, 4122, F64, 40) (dual of [4122, 4035, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(30) [i] based on
- linear OA(6479, 4096, F64, 40) (dual of [4096, 4017, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(6461, 4096, F64, 31) (dual of [4096, 4035, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(648, 26, F64, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,64)), using
- discarding factors / shortening the dual code based on linear OA(648, 64, F64, 8) (dual of [64, 56, 9]-code or 64-arc in PG(7,64)), using
- Reed–Solomon code RS(56,64) [i]
- discarding factors / shortening the dual code based on linear OA(648, 64, F64, 8) (dual of [64, 56, 9]-code or 64-arc in PG(7,64)), using
- construction X applied to Ce(39) ⊂ Ce(30) [i] based on
- discarding factors / shortening the dual code based on linear OA(6487, 4122, F64, 40) (dual of [4122, 4035, 41]-code), using
(47, 87, large)-Net in Base 64 — Upper bound on s
There is no (47, 87, large)-net in base 64, because
- 38 times m-reduction [i] would yield (47, 49, large)-net in base 64, but