MinT - Best Known (59−48, 59, s)-Nets in Base 64

Best Known (59−48, 59, s)-Nets in Base 64

(59−48, 59, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 59, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 59, 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]

(59−48, 59, 225)-Net over F₆₄ — Digital

Digital (11, 59, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 59, 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]

(59−48, 59, 4275)-Net in Base 64 — Upper bound on s

There is no (11, 59, 4276)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 36751 636054 129280 407533 254329 869449 642255 959808 922407 120611 860962 501115 456559 392509 440340 638867 773887 652796 > 64⁵⁹ [i]