MinT - Best Known (187−36, 187, s)-Nets in Base 4

Best Known (187−36, 187, s)-Nets in Base 4

(187−36, 187, 1104)-Net over F₄ — Constructive and digital

Digital (151, 187, 1104)-net over F₄, using

4¹ times duplication [i] based on digital (150, 186, 1104)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (24, 42, 76)-net over F₄, using
    - trace code for nets [i] based on digital (3, 21, 38)-net over F₁₆, using
      - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
        a function field by SÃ©mirat [i]
  2. digital (108, 144, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 36, 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]

(187−36, 187, 7653)-Net over F₄ — Digital

Digital (151, 187, 7653)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(187−36, 187, 4526283)-Net in Base 4 — Upper bound on s

There is no (151, 187, 4526284)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 38478 577603 995063 078196 834174 879665 386005 666958 476655 479896 014592 558563 911819 374712 084084 698574 005974 701772 170276 > 4¹⁸⁷ [i]