MinT - Best Known (162, 202, s)-Nets in Base 4

Best Known (162, 202, s)-Nets in Base 4

(162, 202, 1076)-Net over F₄ — Constructive and digital

Digital (162, 202, 1076)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (22, 42, 48)-net over F₄, using
  - trace code for nets [i] based on digital (1, 21, 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 (120, 160, 1028)-net over F₄, using
  - trace code for nets [i] based on digital (0, 40, 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]

(162, 202, 6759)-Net over F₄ — Digital

Digital (162, 202, 6759)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 202, 3334178)-Net in Base 4 — Upper bound on s

There is no (162, 202, 3334179)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 41 316243 617842 713118 123210 597703 869748 760247 868136 638886 855929 805551 372333 191233 364103 293151 048502 203024 782070 172403 637656 > 4²⁰² [i]