MinT - Best Known (78−69, 78, s)-Nets in Base 64

Best Known (78−69, 78, s)-Nets in Base 64

(78−69, 78, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 78, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 78, 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]

(78−69, 78, 209)-Net over F₆₄ — Digital

Digital (9, 78, 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]

(78−69, 78, 2629)-Net in Base 64 — Upper bound on s

There is no (9, 78, 2630)-net in base 64, because

1 times m-reduction [i] would yield (9, 77, 2630)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 12 054495 550726 801252 838965 071947 297713 335744 776844 188067 059716 040140 240685 956712 601464 448561 066854 213313 536191 047333 682591 524942 443084 691676 > 64⁷⁷ [i]