MinT - Best Known (10, 41, s)-Nets in Base 64

Best Known (10, 41, s)-Nets in Base 64

(10, 41, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 41, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 41, 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, 41, 192)-Net in Base 64 — Constructive

(10, 41, 192)-net in base 64, using

8 times m-reduction [i] based on (10, 49, 192)-net in base 64, using
- base change [i] based on digital (3, 42, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(10, 41, 225)-Net over F₆₄ — Digital

Digital (10, 41, 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, 41, 6674)-Net in Base 64 — Upper bound on s

There is no (10, 41, 6675)-net in base 64, because

1 times m-reduction [i] would yield (10, 40, 6675)-net in base 64, but
- 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]