MinT - Best Known (80−68, 80, s)-Nets in Base 64

Best Known (80−68, 80, s)-Nets in Base 64

(80−68, 80, 177)-Net over F₆₄ — Constructive and digital

Digital (12, 80, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 80, 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]

(80−68, 80, 257)-Net over F₆₄ — Digital

Digital (12, 80, 257)-net over F₆₄, using

net from sequence [i] based on digital (12, 256)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 12 and N(F) ≥ 257, using
  - K_1,2 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

(80−68, 80, 3802)-Net in Base 64 — Upper bound on s

There is no (12, 80, 3803)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 145313 813200 941774 286101 457616 914232 635103 294821 871998 489850 278676 829404 134460 385292 294198 848859 909325 558726 922119 482371 215102 645181 181387 257670 > 64⁸⁰ [i]