MinT - Best Known (80−66, 80, s)-Nets in Base 64

Best Known (80−66, 80, s)-Nets in Base 64

(80−66, 80, 177)-Net over F₆₄ — Constructive and digital

Digital (14, 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]

(80−66, 80, 257)-Net over F₆₄ — Digital

Digital (14, 80, 257)-net over F₆₄, using

t-expansion [i] based on 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]

(80−66, 80, 4979)-Net in Base 64 — Upper bound on s

There is no (14, 80, 4980)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 130143 621662 925260 246093 078551 618190 586499 506104 705052 802143 699880 550797 578891 442637 580300 304537 966665 434534 760512 970044 356744 080431 443150 782589 > 64⁸⁰ [i]