MinT - Best Known (9, 9+59, s)-Nets in Base 64

Best Known (9, 9+59, s)-Nets in Base 64

(9, 9+59, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 68, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 68, 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]

(9, 9+59, 209)-Net over F₆₄ — Digital

Digital (9, 68, 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]

(9, 9+59, 2744)-Net in Base 64 — Upper bound on s

There is no (9, 68, 2745)-net in base 64, because

1 times m-reduction [i] would yield (9, 67, 2745)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 10 427228 006975 775756 051787 985777 344796 038929 536080 645858 419135 092475 705189 926334 547763 770784 372031 377545 567804 552461 174496 > 64⁶⁷ [i]