MinT - Best Known (192−38, 192, s)-Nets in Base 4

Best Known (192−38, 192, s)-Nets in Base 4

(192−38, 192, 1076)-Net over F₄ — Constructive and digital

Digital (154, 192, 1076)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (21, 40, 48)-net over F₄, using
  - trace code for nets [i] based on digital (1, 20, 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 (114, 152, 1028)-net over F₄, using
  - trace code for nets [i] based on digital (0, 38, 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]

(192−38, 192, 6519)-Net over F₄ — Digital

Digital (154, 192, 6519)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(192−38, 192, 3206762)-Net in Base 4 — Upper bound on s

There is no (154, 192, 3206763)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 39 402074 704757 555224 543141 497477 479744 854935 820774 621964 516075 727982 684315 287643 807293 888224 821099 873719 734810 073400 > 4¹⁹² [i]