MinT - Best Known (185−70, 185, s)-Nets in Base 3

Best Known (185−70, 185, s)-Nets in Base 3

(185−70, 185, 156)-Net over F₃ — Constructive and digital

Digital (115, 185, 156)-net over F₃, using

1 times m-reduction [i] based on digital (115, 186, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 93, 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]

(185−70, 185, 205)-Net over F₃ — Digital

Digital (115, 185, 205)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−70, 185, 2278)-Net in Base 3 — Upper bound on s

There is no (115, 185, 2279)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18614 413046 658217 027696 882133 075192 655209 697988 829111 581290 359647 872131 141390 900444 190555 > 3¹⁸⁵ [i]