Best Known (32, 89, s)-Nets in Base 64
(32, 89, 513)-Net over F64 — Constructive and digital
Digital (32, 89, 513)-net over F64, using
- t-expansion [i] based on digital (28, 89, 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
(32, 89, 85144)-Net in Base 64 — Upper bound on s
There is no (32, 89, 85145)-net in base 64, because
- 1 times m-reduction [i] would yield (32, 88, 85145)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 878 702876 551373 264282 427048 238482 765675 031462 485647 276526 598718 003744 096245 224689 782034 200451 269168 303595 458585 097302 983188 012478 255566 590587 587899 760011 686304 > 6488 [i]