Best Known (36, 36+55, s)-Nets in Base 64
(36, 36+55, 513)-Net over F64 — Constructive and digital
Digital (36, 91, 513)-net over F64, using
- t-expansion [i] based on digital (28, 91, 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
(36, 36+55, 181816)-Net in Base 64 — Upper bound on s
There is no (36, 91, 181817)-net in base 64, because
- 1 times m-reduction [i] would yield (36, 90, 181817)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 3 599226 809821 094349 642345 779374 287473 016000 327781 013364 937330 500635 496584 753496 417777 686684 673563 254663 993969 102794 218302 078894 136646 542396 762263 210028 809834 146400 > 6490 [i]