Best Known (87−58, 87, s)-Nets in Base 64
(87−58, 87, 513)-Net over F64 — Constructive and digital
Digital (29, 87, 513)-net over F64, using
- t-expansion [i] based on digital (28, 87, 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
(87−58, 87, 48550)-Net in Base 64 — Upper bound on s
There is no (29, 87, 48551)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 13 735189 842151 405432 389751 721817 479687 798440 070538 255529 571703 662530 831751 702917 895368 084079 269439 096521 667668 398337 281091 833102 174729 627841 323822 120800 696680 > 6487 [i]