MinT - Best Known (182−36, 182, s)-Nets in Base 4

Best Known (182−36, 182, s)-Nets in Base 4

(182−36, 182, 1076)-Net over F₄ — Constructive and digital

Digital (146, 182, 1076)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (20, 38, 48)-net over F₄, using
  - trace code for nets [i] based on digital (1, 19, 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 (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]

(182−36, 182, 6281)-Net over F₄ — Digital

Digital (146, 182, 6281)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−36, 182, 3079656)-Net in Base 4 — Upper bound on s

There is no (146, 182, 3079657)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 37 576874 676915 836710 864675 973225 535654 245450 303285 738216 185345 872435 269354 889820 545349 621096 311872 871341 021944 > 4¹⁸² [i]