Best Known (7, 7+21, s)-Nets in Base 64
(7, 7+21, 177)-Net over F64 — Constructive and digital
Digital (7, 28, 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
(7, 7+21, 257)-Net in Base 64 — Constructive
(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
(7, 7+21, 5406)-Net in Base 64 — Upper bound on s
There is no (7, 28, 5407)-net in base 64, because
- 1 times m-reduction [i] would yield (7, 27, 5407)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 5 847170 471135 912143 706139 894914 030757 811742 248375 > 6427 [i]