Best Known (62−46, 62, s)-Nets in Base 64
(62−46, 62, 177)-Net over F64 — Constructive and digital
Digital (16, 62, 177)-net over F64, using
- t-expansion [i] based on digital (7, 62, 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
(62−46, 62, 257)-Net in Base 64 — Constructive
(16, 62, 257)-net in base 64, using
- 2 times m-reduction [i] based on (16, 64, 257)-net in base 64, using
- base change [i] based on digital (0, 48, 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, 48, 257)-net over F256, using
(62−46, 62, 267)-Net over F64 — Digital
Digital (16, 62, 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
(62−46, 62, 11053)-Net in Base 64 — Upper bound on s
There is no (16, 62, 11054)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 9628 270134 657921 691572 771116 549778 507565 363778 288282 934849 345146 785253 770624 884998 229764 400327 282173 231422 982632 > 6462 [i]