MinT - Best Known (184−36, 184, s)-Nets in Base 4

Best Known (184−36, 184, s)-Nets in Base 4

(184−36, 184, 1094)-Net over F₄ — Constructive and digital

Digital (148, 184, 1094)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (22, 40, 66)-net over F₄, using
  - trace code for nets [i] based on digital (2, 20, 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 (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]

(184−36, 184, 6798)-Net over F₄ — Digital

Digital (148, 184, 6798)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−36, 184, 3592510)-Net in Base 4 — Upper bound on s

There is no (148, 184, 3592511)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 601 227774 401407 175014 760355 894407 998272 064293 665053 738159 840321 279944 209587 259869 269396 393391 810063 996372 460215 > 4¹⁸⁴ [i]