Best Known (87−54, 87, s)-Nets in Base 64
(87−54, 87, 513)-Net over F64 — Constructive and digital
Digital (33, 87, 513)-net over F64, using
- t-expansion [i] based on digital (28, 87, 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
(87−54, 87, 114532)-Net in Base 64 — Upper bound on s
There is no (33, 87, 114533)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 13 731372 258500 810571 359438 134091 170152 611264 022869 025485 083776 820666 016963 175877 610697 329044 199859 069833 079981 667359 944537 986041 072713 946596 263794 985160 244016 > 6487 [i]