MinT - Best Known (147, 147+36, s)-Nets in Base 4

Best Known (147, 147+36, s)-Nets in Base 4

(147, 147+36, 1076)-Net over F₄ — Constructive and digital

Digital (147, 183, 1076)-net over F₄, using

4¹ times duplication [i] based on digital (146, 182, 1076)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (20, 38, 48)-net over F₄, using
    - trace code for nets [i] based on digital (1, 19, 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 (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]

(147, 147+36, 6534)-Net over F₄ — Digital

Digital (147, 183, 6534)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+36, 3326213)-Net in Base 4 — Upper bound on s

There is no (147, 183, 3326214)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 150 306932 456282 582323 172447 491167 662179 442786 115536 940960 252362 997854 612926 365955 405833 125457 503555 598102 523360 > 4¹⁸³ [i]