MinT - Best Known (174−34, 174, s)-Nets in Base 4

Best Known (174−34, 174, s)-Nets in Base 4

(174−34, 174, 1094)-Net over F₄ — Constructive and digital

Digital (140, 174, 1094)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (21, 38, 66)-net over F₄, using
  - trace code for nets [i] based on digital (2, 19, 33)-net over F₁₆, using
    - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, 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]

(174−34, 174, 6574)-Net over F₄ — Digital

Digital (140, 174, 6574)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−34, 174, 3476028)-Net in Base 4 — Upper bound on s

There is no (140, 174, 3476029)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 573 375973 444043 452136 532907 844713 986738 689353 280926 809900 263799 423469 811150 813724 211613 374125 804960 870760 > 4¹⁷⁴ [i]