MinT - Best Known (186−36, 186, s)-Nets in Base 4

Best Known (186−36, 186, s)-Nets in Base 4

(186−36, 186, 1104)-Net over F₄ — Constructive and digital

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]

(186−36, 186, 7357)-Net over F₄ — Digital

Digital (150, 186, 7357)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−36, 186, 4190770)-Net in Base 4 — Upper bound on s

There is no (150, 186, 4190771)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9619 651779 653443 475254 892330 688574 280961 829660 418648 688062 311015 996895 156226 741818 726760 774723 709372 801339 022359 > 4¹⁸⁶ [i]