MinT - Best Known (11, 75, s)-Nets in Base 64

Best Known (11, 75, s)-Nets in Base 64

(11, 75, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 75, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 75, 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]

(11, 75, 225)-Net over F₆₄ — Digital

Digital (11, 75, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 75, 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]

(11, 75, 3457)-Net in Base 64 — Upper bound on s

There is no (11, 75, 3458)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2919 129551 868017 592572 509211 937157 582286 916158 441608 108152 956392 098415 649312 268215 978961 760454 928557 756998 125173 583013 466349 855360 024628 > 64⁷⁵ [i]