MinT - Best Known (68−42, 68, s)-Nets in Base 9

Best Known (68−42, 68, s)-Nets in Base 9

(68−42, 68, 78)-Net over F₉ — Constructive and digital

Digital (26, 68, 78)-net over F₉, using

t-expansion [i] based on digital (22, 68, 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]

(68−42, 68, 110)-Net over F₉ — Digital

Digital (26, 68, 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]

(68−42, 68, 1321)-Net in Base 9 — Upper bound on s

There is no (26, 68, 1322)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 77418 720649 470108 406410 339630 529658 803893 965177 226232 517797 180177 > 9⁶⁸ [i]