MinT - Best Known (126, 232, s)-Nets in Base 3

Best Known (126, 232, s)-Nets in Base 3

(126, 232, 85)-Net over F₃ — Constructive and digital

Digital (126, 232, 85)-net over F₃, using

2 times m-reduction [i] based on digital (126, 234, 85)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (27, 81, 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, 153, 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]

(126, 232, 147)-Net over F₃ — Digital

Digital (126, 232, 147)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 232, 1211)-Net in Base 3 — Upper bound on s

There is no (126, 232, 1212)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 511 881297 410917 082429 201749 094844 004671 470099 080989 776951 621579 530562 893430 449504 128996 244651 210162 798271 892057 > 3²³² [i]