MinT - Best Known (10, 10+81, s)-Nets in Base 64

Best Known (10, 10+81, s)-Nets in Base 64

(10, 10+81, 177)-Net over F₆₄ — Constructive and digital

Digital (10, 91, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 91, 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, 10+81, 225)-Net over F₆₄ — Digital

Digital (10, 91, 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, 10+81, 2879)-Net in Base 64 — Upper bound on s

There is no (10, 91, 2880)-net in base 64, because

1 times m-reduction [i] would yield (10, 90, 2880)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 3 618608 055326 223998 026768 415293 597308 785195 184083 137038 752114 295729 754841 437775 698056 131551 015768 239604 985484 394725 607192 723788 261679 727074 226412 550333 112145 673171 > 64⁹⁰ [i]