Best Known (86−58, 86, s)-Nets in Base 64
(86−58, 86, 513)-Net over F64 — Constructive and digital
Digital (28, 86, 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
(86−58, 86, 42062)-Net in Base 64 — Upper bound on s
There is no (28, 86, 42063)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 214670 749190 301276 127982 689147 728337 388655 919732 000842 543552 399083 905661 962478 748222 934956 278823 029789 346651 692449 657360 596168 660721 951921 243225 076490 337960 > 6486 [i]