MinT - Best Known (90−58, 90, s)-Nets in Base 64

Best Known (90−58, 90, s)-Nets in Base 64

(90−58, 90, 513)-Net over F₆₄ — Constructive and digital

Digital (32, 90, 513)-net over F₆₄, using

t-expansion [i] based on digital (28, 90, 513)-net over F₆₄, using
- net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(90−58, 90, 74659)-Net in Base 64 — Upper bound on s

There is no (32, 90, 74660)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 600208 931560 093735 361796 034586 466552 673474 916926 564870 989118 267274 070098 608509 372663 795872 212395 631974 239792 772621 998335 410053 580939 415038 492725 071271 113766 088232 > 64⁹⁰ [i]