MinT - Best Known (11, 42, s)-Nets in Base 64

Best Known (11, 42, s)-Nets in Base 64

(11, 42, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 42, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 42, 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, 42, 225)-Net over F₆₄ — Digital

Digital (11, 42, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 42, 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, 42, 257)-Net in Base 64 — Constructive

(11, 42, 257)-net in base 64, using

2 times m-reduction [i] based on (11, 44, 257)-net in base 64, using
- base change [i] based on digital (0, 33, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(11, 42, 8809)-Net in Base 64 — Upper bound on s

There is no (11, 42, 8810)-net in base 64, because

1 times m-reduction [i] would yield (11, 41, 8810)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 113 134804 926713 435491 125743 432597 808968 984355 889483 405367 239138 760965 020688 > 64⁴¹ [i]