MinT - Best Known (143, 143+85, s)-Nets in Base 3

Best Known (143, 143+85, s)-Nets in Base 3

(143, 143+85, 156)-Net over F₃ — Constructive and digital

Digital (143, 228, 156)-net over F₃, using

14 times m-reduction [i] based on digital (143, 242, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 121, 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]

(143, 143+85, 257)-Net over F₃ — Digital

Digital (143, 228, 257)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+85, 3088)-Net in Base 3 — Upper bound on s

There is no (143, 228, 3089)-net in base 3, because

1 times m-reduction [i] would yield (143, 227, 3089)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 041872 755128 200376 982891 811519 557408 585687 881685 500720 226674 594232 218337 497379 506949 956118 279238 227032 668873 > 3²²⁷ [i]