MinT - Best Known (90−65, 90, s)-Nets in Base 9

Best Known (90−65, 90, s)-Nets in Base 9

(90−65, 90, 78)-Net over F₉ — Constructive and digital

Digital (25, 90, 78)-net over F₉, using

t-expansion [i] based on digital (22, 90, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(90−65, 90, 96)-Net over F₉ — Digital

Digital (25, 90, 96)-net over F₉, using

net from sequence [i] based on digital (25, 95)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 25 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(90−65, 90, 701)-Net in Base 9 — Upper bound on s

There is no (25, 90, 702)-net in base 9, because

1 times m-reduction [i] would yield (25, 89, 702)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 695630 366651 883416 494502 011456 603583 605818 680996 671717 653017 827437 496251 729033 542145 > 9⁸⁹ [i]