MinT - Best Known (80−53, 80, s)-Nets in Base 9

Best Known (80−53, 80, s)-Nets in Base 9

(80−53, 80, 78)-Net over F₉ — Constructive and digital

Digital (27, 80, 78)-net over F₉, using

t-expansion [i] based on digital (22, 80, 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]

(80−53, 80, 110)-Net over F₉ — Digital

Digital (27, 80, 110)-net over F₉, using

t-expansion [i] based on digital (26, 80, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(80−53, 80, 1030)-Net in Base 9 — Upper bound on s

There is no (27, 80, 1031)-net in base 9, because

1 times m-reduction [i] would yield (27, 79, 1031)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2454 038484 529238 533427 658019 720671 096601 305057 254921 442186 016105 006970 874033 > 9⁷⁹ [i]