MinT - Best Known (54−44, 54, s)-Nets in Base 64

Best Known (54−44, 54, s)-Nets in Base 64

(54−44, 54, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 54, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 54, 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]

(54−44, 54, 225)-Net over F₆₄ — Digital

Digital (10, 54, 225)-net over F₆₄, using

net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
  - a curve from the manYPoints database [i]

(54−44, 54, 3887)-Net in Base 64 — Upper bound on s

There is no (10, 54, 3888)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 34 301424 560231 982072 134189 899997 230033 535694 651478 672445 817309 195747 198098 072678 764902 623673 254338 > 64⁵⁴ [i]