Best Known (50−22, 50, s)-Nets in Base 64
(50−22, 50, 513)-Net over F64 — Constructive and digital
Digital (28, 50, 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
(50−22, 50, 518)-Net in Base 64 — Constructive
(28, 50, 518)-net in base 64, using
- (u, u+v)-construction [i] based on
- (7, 18, 259)-net in base 64, using
- 2 times m-reduction [i] based on (7, 20, 259)-net in base 64, using
- base change [i] based on digital (2, 15, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 15, 259)-net over F256, using
- 2 times m-reduction [i] based on (7, 20, 259)-net in base 64, using
- (10, 32, 259)-net in base 64, using
- base change [i] based on digital (2, 24, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256 (see above)
- base change [i] based on digital (2, 24, 259)-net over F256, using
- (7, 18, 259)-net in base 64, using
(50−22, 50, 3499)-Net over F64 — Digital
Digital (28, 50, 3499)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6450, 3499, F64, 22) (dual of [3499, 3449, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6450, 4119, F64, 22) (dual of [4119, 4069, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(21) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(6450, 4119, F64, 22) (dual of [4119, 4069, 23]-code), using
(50−22, 50, large)-Net in Base 64 — Upper bound on s
There is no (28, 50, large)-net in base 64, because
- 20 times m-reduction [i] would yield (28, 30, large)-net in base 64, but