MinT - Best Known (95−65, 95, s)-Nets in Base 9

Best Known (95−65, 95, s)-Nets in Base 9

(95−65, 95, 78)-Net over F₉ — Constructive and digital

Digital (30, 95, 78)-net over F₉, using

t-expansion [i] based on digital (22, 95, 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]

(95−65, 95, 110)-Net over F₉ — Digital

Digital (30, 95, 110)-net over F₉, using

t-expansion [i] based on digital (26, 95, 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]

(95−65, 95, 996)-Net in Base 9 — Upper bound on s

There is no (30, 95, 997)-net in base 9, because

1 times m-reduction [i] would yield (30, 94, 997)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 506575 009722 137449 137145 905389 464888 319553 090407 393098 287436 779783 077244 599271 151196 121345 > 9⁹⁴ [i]