MinT - Best Known (146−28, 146, s)-Nets in Base 4

Best Known (146−28, 146, s)-Nets in Base 4

(146−28, 146, 1104)-Net over F₄ — Constructive and digital

Digital (118, 146, 1104)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (20, 34, 76)-net over F₄, using
  - trace code for nets [i] based on digital (3, 17, 38)-net over F₁₆, using
    - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, 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]

(146−28, 146, 6573)-Net over F₄ — Digital

Digital (118, 146, 6573)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−28, 146, 3827902)-Net in Base 4 — Upper bound on s

There is no (118, 146, 3827903)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7957 192935 154681 547554 187258 581779 513679 832266 468007 189710 217791 960249 816240 484813 421871 > 4¹⁴⁶ [i]