MinT - Best Known (117, 145, s)-Nets in Base 4

Best Known (117, 145, s)-Nets in Base 4

(117, 145, 1094)-Net over F₄ — Constructive and digital

Digital (117, 145, 1094)-net over F₄, using

4¹ times duplication [i] based on digital (116, 144, 1094)-net over F₄, using
- (u,Â u+v)-construction [i] based on
  1. digital (18, 32, 66)-net over F₄, using
    - trace code for nets [i] based on digital (2, 16, 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 (84, 112, 1028)-net over F₄, using
    - trace code for nets [i] based on digital (0, 28, 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]

(117, 145, 6244)-Net over F₄ — Digital

Digital (117, 145, 6244)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 145, 3467020)-Net in Base 4 — Upper bound on s

There is no (117, 145, 3467021)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1989 295993 772267 955268 384900 041044 956751 010965 076362 878901 810994 322098 424557 726035 166256 > 4¹⁴⁵ [i]