MinT - Best Known (9, 9+57, s)-Nets in Base 64

Best Known (9, 9+57, s)-Nets in Base 64

(9, 9+57, 177)-Net over F₆₄ — Constructive and digital

Digital (9, 66, 177)-net over F₆₄, using

t-expansion [i] based on digital (7, 66, 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+57, 209)-Net over F₆₄ — Digital

Digital (9, 66, 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+57, 2782)-Net in Base 64 — Upper bound on s

There is no (9, 66, 2783)-net in base 64, because

1 times m-reduction [i] would yield (9, 65, 2783)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 2537 943363 454765 292767 125127 985273 594348 506777 488657 213477 541872 176141 558682 626077 328437 541982 926344 114801 701937 846135 > 64⁶⁵ [i]