Best Known (37−20, 37, s)-Nets in Base 64
(37−20, 37, 242)-Net over F64 — Constructive and digital
Digital (17, 37, 242)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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 (7, 27, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- digital (0, 10, 65)-net over F64, using
(37−20, 37, 322)-Net in Base 64 — Constructive
(17, 37, 322)-net in base 64, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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
- (7, 27, 257)-net in base 64, using
- 1 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- base change [i] based on digital (0, 21, 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, 21, 257)-net over F256, using
- 1 times m-reduction [i] based on (7, 28, 257)-net in base 64, using
- digital (0, 10, 65)-net over F64, using
(37−20, 37, 483)-Net over F64 — Digital
Digital (17, 37, 483)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6437, 483, F64, 20) (dual of [483, 446, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(6437, 585, F64, 20) (dual of [585, 548, 21]-code), using
(37−20, 37, 346334)-Net in Base 64 — Upper bound on s
There is no (17, 37, 346335)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 6 740074 675254 832842 997049 991399 035011 783467 842168 763813 124488 064735 > 6437 [i]