MinT - Best Known (31, 31+28, s)-Nets in Base 4

Best Known (31, 31+28, s)-Nets in Base 4

(31, 31+28, 48)-Net over F₄ — Constructive and digital

Digital (31, 59, 48)-net over F₄, using

1 times m-reduction [i] based on digital (31, 60, 48)-net over F₄, using
- trace code for nets [i] based on digital (1, 30, 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]

(31, 31+28, 64)-Net over F₄ — Digital

Digital (31, 59, 64)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(31, 31+28, 683)-Net in Base 4 — Upper bound on s

There is no (31, 59, 684)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 337231 403268 843129 217295 718234 029320 > 4⁵⁹ [i]