Best Known (59−44, 59, s)-Nets in Base 64
(59−44, 59, 177)-Net over F64 — Constructive and digital
Digital (15, 59, 177)-net over F64, using
- t-expansion [i] based on digital (7, 59, 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
(59−44, 59, 257)-Net in Base 64 — Constructive
(15, 59, 257)-net in base 64, using
- 1 times m-reduction [i] based on (15, 60, 257)-net in base 64, using
- base change [i] based on digital (0, 45, 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, 45, 257)-net over F256, using
(59−44, 59, 258)-Net over F64 — Digital
Digital (15, 59, 258)-net over F64, using
- net from sequence [i] based on digital (15, 257)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 15 and N(F) ≥ 258, using
(59−44, 59, 10020)-Net in Base 64 — Upper bound on s
There is no (15, 59, 10021)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 36737 122060 882410 149388 598616 946965 551658 448189 360430 688661 736052 278148 719736 949685 307811 009463 090225 446256 > 6459 [i]