MinT - Best Known (246−93, 246, s)-Nets in Base 3

Best Known (246−93, 246, s)-Nets in Base 3

(246−93, 246, 156)-Net over F₃ — Constructive and digital

Digital (153, 246, 156)-net over F₃, using

t-expansion [i] based on digital (147, 246, 156)-net over F₃, using
- 4 times m-reduction [i] based on digital (147, 250, 156)-net over F₃, using
  - trace code for nets [i] based on digital (22, 125, 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]

(246−93, 246, 263)-Net over F₃ — Digital

Digital (153, 246, 263)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−93, 246, 3083)-Net in Base 3 — Upper bound on s

There is no (153, 246, 3084)-net in base 3, because

1 times m-reduction [i] would yield (153, 245, 3084)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 788 695404 633751 606411 297806 443357 763060 342186 272908 988334 878971 435409 868947 951703 371902 376760 691732 238625 873757 719177 > 3²⁴⁵ [i]