Best Known (20, 86, s)-Nets in Base 64
(20, 86, 177)-Net over F64 — Constructive and digital
Digital (20, 86, 177)-net over F64, using
- t-expansion [i] based on digital (7, 86, 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
(20, 86, 216)-Net in Base 64 — Constructive
(20, 86, 216)-net in base 64, using
- t-expansion [i] based on (18, 86, 216)-net in base 64, using
- 5 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 78, 216)-net over F128, using
- 5 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
(20, 86, 342)-Net over F64 — Digital
Digital (20, 86, 342)-net over F64, using
- net from sequence [i] based on digital (20, 341)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 20 and N(F) ≥ 342, using
(20, 86, 10625)-Net in Base 64 — Upper bound on s
There is no (20, 86, 10626)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 214792 166042 005204 859480 521543 360044 813447 331681 620675 229598 926941 667363 873772 920443 370111 408529 642517 993627 765437 134703 490688 646149 459297 980554 115639 651244 > 6486 [i]