Best Known (49, 89, s)-Nets in Base 64
(49, 89, 593)-Net over F64 — Constructive and digital
Digital (49, 89, 593)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (1, 21, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- 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
- digital (1, 21, 80)-net over F64, using
(49, 89, 3614)-Net over F64 — Digital
Digital (49, 89, 3614)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6489, 3614, F64, 40) (dual of [3614, 3525, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(6489, 4128, F64, 40) (dual of [4128, 4039, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(28) [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(6457, 4096, F64, 29) (dual of [4096, 4039, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(39) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(6489, 4128, F64, 40) (dual of [4128, 4039, 41]-code), using
(49, 89, large)-Net in Base 64 — Upper bound on s
There is no (49, 89, large)-net in base 64, because
- 38 times m-reduction [i] would yield (49, 51, large)-net in base 64, but