MinT - Best Known (10, 40, s)-Nets in Base 64

Best Known (10, 40, s)-Nets in Base 64

(10, 40, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 40, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 40, 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]

(10, 40, 225)-Net over F₆₄ — Digital

Digital (10, 40, 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]

(10, 40, 257)-Net in Base 64 — Constructive

(10, 40, 257)-net in base 64, using

base change [i] based on digital (0, 30, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(10, 40, 6674)-Net in Base 64 — Upper bound on s

There is no (10, 40, 6675)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 1 767812 544863 240051 830513 496623 451280 843257 540360 830331 952067 921590 475216 > 64⁴⁰ [i]