MinT - Best Known (65−54, 65, s)-Nets in Base 64

Best Known (65−54, 65, s)-Nets in Base 64

(65−54, 65, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 65, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 65, 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]

(65−54, 65, 225)-Net over F₆₄ — Digital

Digital (11, 65, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 65, 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]

(65−54, 65, 3852)-Net in Base 64 — Upper bound on s

There is no (11, 65, 3853)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2526 699472 654092 940889 153381 379889 371548 853126 747026 173660 701248 525142 176740 647794 439907 504116 846030 071061 114362 830528 > 64⁶⁵ [i]