MinT - Best Known (56−26, 56, s)-Nets in Base 3

Best Known (56−26, 56, s)-Nets in Base 3

(56−26, 56, 40)-Net over F₃ — Constructive and digital

Digital (30, 56, 40)-net over F₃, using

trace code for nets [i] based on digital (2, 28, 20)-net over F₉, using
- net from sequence [i] based on digital (2, 19)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
    - a function field by GarcÃa and Quoos [i]

(56−26, 56, 46)-Net over F₃ — Digital

Digital (30, 56, 46)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−26, 56, 309)-Net in Base 3 — Upper bound on s

There is no (30, 56, 310)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 532 729868 150153 808260 411061 > 3⁵⁶ [i]