MinT - Best Known (191−94, 191, s)-Nets in Base 3

Best Known (191−94, 191, s)-Nets in Base 3

(191−94, 191, 69)-Net over F₃ — Constructive and digital

Digital (97, 191, 69)-net over F₃, using

4 times m-reduction [i] based on digital (97, 195, 69)-net over F₃, using
- (u,Â u+v)-construction [i] based on
  1. digital (21, 70, 32)-net over F₃, using
    - net from sequence [i] based on digital (21, 31)-sequence over F₃, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
        an explicitly constructive algebraic function field [i]
  2. digital (27, 125, 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]

(191−94, 191, 101)-Net over F₃ — Digital

Digital (97, 191, 101)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−94, 191, 752)-Net in Base 3 — Upper bound on s

There is no (97, 191, 753)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 811637 796834 905446 456777 737824 711235 339702 116152 734446 244964 576896 713876 168692 322761 867691 > 3¹⁹¹ [i]