MinT - Best Known (64−53, 64, s)-Nets in Base 64

Best Known (64−53, 64, s)-Nets in Base 64

(64−53, 64, 177)-Net over F₆₄ — Constructive and digital

Digital (11, 64, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 64, 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]

(64−53, 64, 225)-Net over F₆₄ — Digital

Digital (11, 64, 225)-net over F₆₄, using

t-expansion [i] based on digital (10, 64, 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]

(64−53, 64, 3972)-Net in Base 64 — Upper bound on s

There is no (11, 64, 3973)-net in base 64, because

1 times m-reduction [i] would yield (11, 63, 3973)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 617922 334826 867784 677924 835001 616780 480791 454035 265134 082555 170673 360998 817754 088700 302553 978403 235910 023159 232800 > 64⁶³ [i]