Best Known (25−18, 25, s)-Nets in Base 64
(25−18, 25, 177)-Net over F64 — Constructive and digital
Digital (7, 25, 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
(25−18, 25, 257)-Net in Base 64 — Constructive
(7, 25, 257)-net in base 64, using
- 3 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
(25−18, 25, 6844)-Net in Base 64 — Upper bound on s
There is no (7, 25, 6845)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 1428 984796 468234 329362 207542 653392 802543 105148 > 6425 [i]