MinT - Best Known (56−47, 56, s)-Nets in Base 64

Best Known (56−47, 56, s)-Nets in Base 64

(56−47, 56, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 56, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 56, 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]

(56−47, 56, 209)-Net over F₆₄ — Digital

Digital (9, 56, 209)-net over F₆₄, using

net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
  - a curve from the manYPoints database [i]

(56−47, 56, 3109)-Net in Base 64 — Upper bound on s

There is no (9, 56, 3110)-net in base 64, because

1 times m-reduction [i] would yield (9, 55, 3110)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2199 057218 953461 957676 653424 864936 658031 173663 837781 201358 954644 135561 179866 601446 907313 186256 754224 > 64⁵⁵ [i]