MinT - Best Known (143, 143+46, s)-Nets in Base 3

Best Known (143, 143+46, s)-Nets in Base 3

(143, 143+46, 400)-Net over F₃ — Constructive and digital

Digital (143, 189, 400)-net over F₃, using

3¹ times duplication [i] based on digital (142, 188, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 47, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(143, 143+46, 905)-Net over F₃ — Digital

Digital (143, 189, 905)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143, 143+46, 39252)-Net in Base 3 — Upper bound on s

There is no (143, 189, 39253)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 499663 150459 917410 064189 323733 427152 069113 077931 580152 790944 774429 779739 624589 845367 404891 > 3¹⁸⁹ [i]