MinT - Best Known (83−74, 83, s)-Nets in Base 64

Best Known (83−74, 83, s)-Nets in Base 64

(83−74, 83, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 83, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 83, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(83−74, 83, 209)-Net over F₆₄ — Digital

Digital (9, 83, 209)-net over F₆₄, using

net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
  - a curve from the manYPoints database [i]

(83−74, 83, 2601)-Net in Base 64 — Upper bound on s

There is no (9, 83, 2602)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 826902 799664 428886 986286 629712 000714 604644 219680 988437 638213 980208 917813 047490 460985 671012 002666 938019 550254 668437 136264 633271 808142 633783 625483 238730 > 64⁸³ [i]