Best Known (12, 12+14, s)-Nets in Base 64
(12, 12+14, 210)-Net over F64 — Constructive and digital
Digital (12, 26, 210)-net over F64, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 4, 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 (0, 7, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64 (see above)
- digital (1, 15, 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 (0, 4, 65)-net over F64, using
(12, 12+14, 322)-Net in Base 64 — Constructive
(12, 26, 322)-net in base 64, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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
- (5, 19, 257)-net in base 64, using
- 1 times m-reduction [i] based on (5, 20, 257)-net in base 64, using
- base change [i] based on digital (0, 15, 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, 15, 257)-net over F256, using
- 1 times m-reduction [i] based on (5, 20, 257)-net in base 64, using
- digital (0, 7, 65)-net over F64, using
(12, 12+14, 481)-Net over F64 — Digital
Digital (12, 26, 481)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6426, 481, F64, 14) (dual of [481, 455, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(6426, 819, F64, 14) (dual of [819, 793, 15]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 819 | 642−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(6426, 819, F64, 14) (dual of [819, 793, 15]-code), using
(12, 12+14, 274310)-Net in Base 64 — Upper bound on s
There is no (12, 26, 274311)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 91346 171937 723768 527106 201172 095312 308710 139200 > 6426 [i]