Best Known (77−49, 77, s)-Nets in Base 64
(77−49, 77, 513)-Net over F64 — Constructive and digital
Digital (28, 77, 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
(77−49, 77, 81569)-Net in Base 64 — Upper bound on s
There is no (28, 77, 81570)-net in base 64, because
- 1 times m-reduction [i] would yield (28, 76, 81570)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 186087 247832 643461 950347 913116 534508 635565 617848 051846 291123 468411 048734 888443 826565 423780 417746 058802 736620 055204 772421 568146 415585 436044 > 6476 [i]