MinT - Best Known (167, 167+68, s)-Nets in Base 4

Best Known (167, 167+68, s)-Nets in Base 4

(167, 167+68, 531)-Net over F₄ — Constructive and digital

Digital (167, 235, 531)-net over F₄, using

5 times m-reduction [i] based on digital (167, 240, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 80, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(167, 167+68, 1107)-Net over F₄ — Digital

Digital (167, 235, 1107)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(167, 167+68, 65383)-Net in Base 4 — Upper bound on s

There is no (167, 235, 65384)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3049 804223 914621 845555 361698 702012 142055 445896 239116 908897 737899 612076 797416 866309 621400 591232 662732 589920 021346 994582 744057 432043 165315 115307 > 4²³⁵ [i]