MinT - Best Known (25−10, 25, s)-Nets in Base 3

Best Known (25−10, 25, s)-Nets in Base 3

(25−10, 25, 40)-Net over F₃ — Constructive and digital

Digital (15, 25, 40)-net over F₃, using

1 times m-reduction [i] based on digital (15, 26, 40)-net over F₃, using
- trace code for nets [i] based on digital (2, 13, 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]

(25−10, 25, 46)-Net over F₃ — Digital

Digital (15, 25, 46)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(25−10, 25, 312)-Net in Base 3 — Upper bound on s

There is no (15, 25, 313)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 860013 499107 > 3²⁵ [i]