MinT - Best Known (84−58, 84, s)-Nets in Base 9

Best Known (84−58, 84, s)-Nets in Base 9

(84−58, 84, 78)-Net over F₉ — Constructive and digital

Digital (26, 84, 78)-net over F₉, using

t-expansion [i] based on digital (22, 84, 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]

(84−58, 84, 110)-Net over F₉ — Digital

Digital (26, 84, 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]

(84−58, 84, 829)-Net in Base 9 — Upper bound on s

There is no (26, 84, 830)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 144 337152 294085 587869 860827 269758 548456 205333 659529 651430 249334 285513 635567 928753 > 9⁸⁴ [i]