Best Known (33, 33+45, s)-Nets in Base 64
(33, 33+45, 513)-Net over F64 — Constructive and digital
Digital (33, 78, 513)-net over F64, using
- t-expansion [i] based on digital (28, 78, 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+45, 301388)-Net in Base 64 — Upper bound on s
There is no (33, 78, 301389)-net in base 64, because
- 1 times m-reduction [i] would yield (33, 77, 301389)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 11 908914 255979 594370 665662 694522 226673 888013 524848 311606 183092 446404 708960 364447 787566 160055 510820 989595 802209 825766 667570 956217 888468 400080 > 6477 [i]