MinT - Best Known (26, 139, s)-Nets in Base 9

Best Known (26, 139, s)-Nets in Base 9

(26, 139, 78)-Net over F₉ — Constructive and digital

Digital (26, 139, 78)-net over F₉, using

t-expansion [i] based on digital (22, 139, 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, 139, 110)-Net over F₉ — Digital

Digital (26, 139, 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, 139, 575)-Net in Base 9 — Upper bound on s

There is no (26, 139, 576)-net in base 9, because

1 times m-reduction [i] would yield (26, 138, 576)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 498171 472405 139571 311081 310640 793044 751542 402594 840577 231004 851738 401081 252669 548671 561398 576126 553186 911671 527835 675117 473848 561665 > 9¹³⁸ [i]