MinT - Best Known (26, 26+108, s)-Nets in Base 9

Best Known (26, 26+108, s)-Nets in Base 9

(26, 26+108, 78)-Net over F₉ — Constructive and digital

Digital (26, 134, 78)-net over F₉, using

t-expansion [i] based on digital (22, 134, 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]

(26, 26+108, 110)-Net over F₉ — Digital

Digital (26, 134, 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]

(26, 26+108, 578)-Net in Base 9 — Upper bound on s

There is no (26, 134, 579)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75 493176 383822 211647 426116 377179 531602 803648 918394 368813 450127 378593 890016 217556 073179 087744 797780 339641 959804 092175 008085 154705 > 9¹³⁴ [i]