Best Known (28, 28+47, s)-Nets in Base 64
(28, 28+47, 513)-Net over F64 — Constructive and digital
Digital (28, 75, 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
(28, 28+47, 96884)-Net in Base 64 — Upper bound on s
There is no (28, 75, 96885)-net in base 64, because
- 1 times m-reduction [i] would yield (28, 74, 96885)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 45 437072 981197 789274 410987 767239 265314 179068 925056 635787 306726 008437 345634 055087 565111 708596 769804 801746 169092 518788 046416 920044 564704 > 6474 [i]