MinT - Best Known (105−78, 105, s)-Nets in Base 9

Best Known (105−78, 105, s)-Nets in Base 9

(105−78, 105, 78)-Net over F₉ — Constructive and digital

Digital (27, 105, 78)-net over F₉, using

t-expansion [i] based on digital (22, 105, 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]

(105−78, 105, 110)-Net over F₉ — Digital

Digital (27, 105, 110)-net over F₉, using

t-expansion [i] based on digital (26, 105, 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]

(105−78, 105, 689)-Net in Base 9 — Upper bound on s

There is no (27, 105, 690)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15728 632856 550603 669613 469080 280546 462382 698677 482058 120867 526378 973211 354738 378752 709143 863248 183985 > 9¹⁰⁵ [i]