MinT - Best Known (139, 173, s)-Nets in Base 4

Best Known (139, 173, s)-Nets in Base 4

(139, 173, 1076)-Net over F₄ — Constructive and digital

Digital (139, 173, 1076)-net over F₄, using

4¹ times duplication [i] based on digital (138, 172, 1076)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (19, 36, 48)-net over F₄, using
    - trace code for nets [i] based on digital (1, 18, 24)-net over F₁₆, using
      - net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
        a function field by SÃ©mirat [i]
  2. digital (102, 136, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 34, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]

(139, 173, 6304)-Net over F₄ — Digital

Digital (139, 173, 6304)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(139, 173, 3203818)-Net in Base 4 — Upper bound on s

There is no (139, 173, 3203819)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 143 344106 940633 217824 069729 533490 748850 221105 724720 146433 968220 584373 585409 778847 637082 366492 107475 930780 > 4¹⁷³ [i]