Best Known (29, 29+46, s)-Nets in Base 64
(29, 29+46, 513)-Net over F64 — Constructive and digital
Digital (29, 75, 513)-net over F64, using
- t-expansion [i] based on digital (28, 75, 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
(29, 29+46, 116088)-Net in Base 64 — Upper bound on s
There is no (29, 75, 116089)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 2907 439280 042513 828199 846912 758049 600101 512883 075479 401515 198161 696274 298440 972235 065829 385447 608052 068076 388674 853063 159546 604250 405912 > 6475 [i]