MinT - Best Known (116, 116+28, s)-Nets in Base 4

Best Known (116, 116+28, s)-Nets in Base 4

(116, 116+28, 1094)-Net over F₄ — Constructive and digital

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]

(116, 116+28, 5932)-Net over F₄ — Digital

Digital (116, 144, 5932)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+28, 3140161)-Net in Base 4 — Upper bound on s

There is no (116, 144, 3140162)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 497 324194 779615 625161 073265 240907 174037 241918 940501 349130 560566 142345 878533 737431 769312 > 4¹⁴⁴ [i]