MinT - Best Known (109−40, 109, s)-Nets in Base 3

Best Known (109−40, 109, s)-Nets in Base 3

(109−40, 109, 128)-Net over F₃ — Constructive and digital

Digital (69, 109, 128)-net over F₃, using

3 times m-reduction [i] based on digital (69, 112, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 56, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(109−40, 109, 145)-Net over F₃ — Digital

Digital (69, 109, 145)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(109−40, 109, 1634)-Net in Base 3 — Upper bound on s

There is no (69, 109, 1635)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10169 720350 007131 810994 850031 934994 279182 339752 694457 > 3¹⁰⁹ [i]