MinT - Best Known (11, 11+63, s)-Nets in Base 64

Best Known (11, 11+63, s)-Nets in Base 64

(11, 11+63, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 74, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 74, 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, 11+63, 225)-Net over F₆₄ — Digital

Digital (11, 74, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 74, 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, 11+63, 3515)-Net in Base 64 — Upper bound on s

There is no (11, 74, 3516)-net in base 64, because

1 times m-reduction [i] would yield (11, 73, 3516)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 709887 098822 205057 277101 357269 647802 375789 392813 327102 115756 262916 360394 279628 362376 716577 825509 671499 391429 039385 330045 679064 627448 > 64⁷³ [i]