Best Known (67−50, 67, s)-Nets in Base 64
(67−50, 67, 177)-Net over F64 — Constructive and digital
Digital (17, 67, 177)-net over F64, using
- t-expansion [i] based on digital (7, 67, 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
(67−50, 67, 257)-Net in Base 64 — Constructive
(17, 67, 257)-net in base 64, using
- 1 times m-reduction [i] based on (17, 68, 257)-net in base 64, using
- base change [i] based on digital (0, 51, 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, 51, 257)-net over F256, using
(67−50, 67, 267)-Net over F64 — Digital
Digital (17, 67, 267)-net over F64, using
- t-expansion [i] based on digital (16, 67, 267)-net over F64, using
- net from sequence [i] based on digital (16, 266)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 16 and N(F) ≥ 267, using
- net from sequence [i] based on digital (16, 266)-sequence over F64, using
(67−50, 67, 11178)-Net in Base 64 — Upper bound on s
There is no (17, 67, 11179)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 10 350772 565610 976753 663744 928425 430949 076819 395442 610335 764215 495391 499538 173140 487711 773565 591310 523543 857549 744730 480220 > 6467 [i]