MinT - Best Known (143−49, 143, s)-Nets in Base 3

Best Known (143−49, 143, s)-Nets in Base 3

(143−49, 143, 156)-Net over F₃ — Constructive and digital

Digital (94, 143, 156)-net over F₃, using

1 times m-reduction [i] based on digital (94, 144, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 72, 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]

(143−49, 143, 221)-Net over F₃ — Digital

Digital (94, 143, 221)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−49, 143, 3237)-Net in Base 3 — Upper bound on s

There is no (94, 143, 3238)-net in base 3, because

1 times m-reduction [i] would yield (94, 142, 3238)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56 729114 921700 644921 150325 963541 228347 362167 774844 648955 502653 629041 > 3¹⁴² [i]