MinT - Best Known (250−116, 250, s)-Nets in Base 3

Best Known (250−116, 250, s)-Nets in Base 3

(250−116, 250, 85)-Net over F₃ — Constructive and digital

Digital (134, 250, 85)-net over F₃, using

t-expansion [i] based on digital (131, 250, 85)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 86, 37)-net over F₃, using
    - net from sequence [i] based on digital (27, 36)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 26, N(F)Â =Â 36, and 1 place with degree 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
  2. digital (45, 164, 48)-net over F₃, using
    - net from sequence [i] based on digital (45, 47)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
        an explicitly constructive algebraic function field [i]

(250−116, 250, 150)-Net over F₃ — Digital

Digital (134, 250, 150)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−116, 250, 1222)-Net in Base 3 — Upper bound on s

There is no (134, 250, 1223)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 197648 083455 934441 941243 174581 604163 172682 905418 551912 233082 835535 607159 143590 572144 907959 437264 551552 553906 397213 826717 > 3²⁵⁰ [i]