MinT - Best Known (112−86, 112, s)-Nets in Base 9

Best Known (112−86, 112, s)-Nets in Base 9

(112−86, 112, 78)-Net over F₉ — Constructive and digital

Digital (26, 112, 78)-net over F₉, using

t-expansion [i] based on digital (22, 112, 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]

(112−86, 112, 110)-Net over F₉ — Digital

Digital (26, 112, 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]

(112−86, 112, 619)-Net in Base 9 — Upper bound on s

There is no (26, 112, 620)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 78267 097472 667021 493773 858737 912780 454753 736750 445276 543683 006434 300205 144790 399126 925376 016149 368717 645217 > 9¹¹² [i]