Best Known (85−38, 85, s)-Nets in Base 64
(85−38, 85, 578)-Net over F64 — Constructive and digital
Digital (47, 85, 578)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 19, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- digital (28, 66, 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
- digital (0, 19, 65)-net over F64, using
(85−38, 85, 3697)-Net over F64 — Digital
Digital (47, 85, 3697)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6485, 3697, F64, 38) (dual of [3697, 3612, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(6485, 4128, F64, 38) (dual of [4128, 4043, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(26) [i] based on
- linear OA(6475, 4096, F64, 38) (dual of [4096, 4021, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(6453, 4096, F64, 27) (dual of [4096, 4043, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(6410, 32, F64, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,64)), using
- discarding factors / shortening the dual code based on linear OA(6410, 64, F64, 10) (dual of [64, 54, 11]-code or 64-arc in PG(9,64)), using
- Reed–Solomon code RS(54,64) [i]
- discarding factors / shortening the dual code based on linear OA(6410, 64, F64, 10) (dual of [64, 54, 11]-code or 64-arc in PG(9,64)), using
- construction X applied to Ce(37) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(6485, 4128, F64, 38) (dual of [4128, 4043, 39]-code), using
(85−38, 85, large)-Net in Base 64 — Upper bound on s
There is no (47, 85, large)-net in base 64, because
- 36 times m-reduction [i] would yield (47, 49, large)-net in base 64, but