MinT - Best Known (78−50, 78, s)-Nets in Base 9

Best Known (78−50, 78, s)-Nets in Base 9

(78−50, 78, 78)-Net over F₉ — Constructive and digital

Digital (28, 78, 78)-net over F₉, using

t-expansion [i] based on digital (22, 78, 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]

(78−50, 78, 110)-Net over F₉ — Digital

Digital (28, 78, 110)-net over F₉, using

t-expansion [i] based on digital (26, 78, 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]

(78−50, 78, 1192)-Net in Base 9 — Upper bound on s

There is no (28, 78, 1193)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 274 723605 362242 229498 949585 292671 538390 177841 947063 435939 422875 542066 158345 > 9⁷⁸ [i]