MinT - Best Known (142−28, 142, s)-Nets in Base 4

Best Known (142−28, 142, s)-Nets in Base 4

(142−28, 142, 1076)-Net over F₄ — Constructive and digital

Digital (114, 142, 1076)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (16, 30, 48)-net over F₄, using
  - trace code for nets [i] based on digital (1, 15, 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 (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]

(142−28, 142, 5355)-Net over F₄ — Digital

Digital (114, 142, 5355)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−28, 142, 2575983)-Net in Base 4 — Upper bound on s

There is no (114, 142, 2575984)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 082778 062688 490074 771913 709923 053185 789015 180396 393105 136100 529909 580753 841992 960835 > 4¹⁴² [i]