Best Known (91−57, 91, s)-Nets in Base 64
(91−57, 91, 513)-Net over F64 — Constructive and digital
Digital (34, 91, 513)-net over F64, using
- t-expansion [i] based on digital (28, 91, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(91−57, 91, 114601)-Net in Base 64 — Upper bound on s
There is no (34, 91, 114602)-net in base 64, because
- 1 times m-reduction [i] would yield (34, 90, 114602)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 599611 022707 094979 286068 140613 545192 132112 243259 432502 146481 410846 811900 656157 450574 946723 543322 595076 626263 531585 972905 003976 005881 443011 630902 747560 319092 372968 > 6490 [i]