Best Known (33, 33+57, s)-Nets in Base 64
(33, 33+57, 513)-Net over F64 — Constructive and digital
Digital (33, 90, 513)-net over F64, using
- t-expansion [i] based on digital (28, 90, 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
(33, 33+57, 98781)-Net in Base 64 — Upper bound on s
There is no (33, 90, 98782)-net in base 64, because
- 1 times m-reduction [i] would yield (33, 89, 98782)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 56245 760983 020594 082756 681901 075057 572975 743628 042671 799767 424261 303932 303495 541982 090487 022108 208441 341854 082207 756817 503907 219712 637982 521472 551441 558516 458121 > 6489 [i]