Best Known (31, 31+54, s)-Nets in Base 64
(31, 31+54, 513)-Net over F64 — Constructive and digital
Digital (31, 85, 513)-net over F64, using
- t-expansion [i] based on digital (28, 85, 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
(31, 31+54, 84162)-Net in Base 64 — Upper bound on s
There is no (31, 85, 84163)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 3352 396402 927165 154206 834350 509791 500339 513076 541835 081845 193976 313439 091441 009857 891438 790621 520908 439624 047048 373658 718515 561913 800114 698695 182351 918016 > 6485 [i]