Best Known (35, 35+54, s)-Nets in Base 64
(35, 35+54, 513)-Net over F64 — Constructive and digital
Digital (35, 89, 513)-net over F64, using
- t-expansion [i] based on digital (28, 89, 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
(35, 35+54, 155859)-Net in Base 64 — Upper bound on s
There is no (35, 89, 155860)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 56241 695944 725971 595153 071268 012173 790515 354357 401626 274570 198940 518718 096065 024064 300014 263265 884729 754077 064603 332118 137983 561602 339727 605349 717203 035057 399016 > 6489 [i]