MinT - Best Known (149, 149+36, s)-Nets in Base 4

Best Known (149, 149+36, s)-Nets in Base 4

(149, 149+36, 1094)-Net over F₄ — Constructive and digital

Digital (149, 185, 1094)-net over F₄, using

4¹ times duplication [i] based on digital (148, 184, 1094)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (22, 40, 66)-net over F₄, using
    - trace code for nets [i] based on digital (2, 20, 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 (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]

(149, 149+36, 7072)-Net over F₄ — Digital

Digital (149, 185, 7072)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+36, 3880127)-Net in Base 4 — Upper bound on s

There is no (149, 185, 3880128)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2404 914963 406021 888725 780295 935985 775465 574340 650358 950670 474511 922892 605204 133629 606271 651204 613896 040942 367325 > 4¹⁸⁵ [i]