Best Known (31, 31+57, s)-Nets in Base 64
(31, 31+57, 513)-Net over F64 — Constructive and digital
Digital (31, 88, 513)-net over F64, using
- t-expansion [i] based on digital (28, 88, 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
(31, 31+57, 73390)-Net in Base 64 — Upper bound on s
There is no (31, 88, 73391)-net in base 64, because
- 1 times m-reduction [i] would yield (31, 87, 73391)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 13 731035 049886 903076 690153 370262 926101 983657 502206 458099 214337 985898 432042 984224 029186 611373 082599 152869 222421 417647 928649 133336 368391 729148 071023 791360 875046 > 6487 [i]