Best Known (87−52, 87, s)-Nets in Base 64
(87−52, 87, 513)-Net over F64 — Constructive and digital
Digital (35, 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
(87−52, 87, 185215)-Net in Base 64 — Upper bound on s
There is no (35, 87, 185216)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 13 729776 277263 548974 281481 654506 784511 062052 999116 078534 554393 647648 235015 413404 933930 867392 541750 994899 810400 965366 231572 114947 304960 108074 134121 292817 365097 > 6487 [i]