MinT - Best Known (125−24, 125, s)-Nets in Base 4

Best Known (125−24, 125, s)-Nets in Base 4

(125−24, 125, 1094)-Net over F₄ — Constructive and digital

Digital (101, 125, 1094)-net over F₄, using

4¹ times duplication [i] based on digital (100, 124, 1094)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (16, 28, 66)-net over F₄, using
    - trace code for nets [i] based on digital (2, 14, 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 (72, 96, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 24, 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]

(125−24, 125, 5891)-Net over F₄ — Digital

Digital (101, 125, 5891)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−24, 125, 3293799)-Net in Base 4 — Upper bound on s

There is no (101, 125, 3293800)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1809 255186 215672 645840 397668 703507 903746 700276 132113 965523 951360 193189 659956 > 4¹²⁵ [i]