MinT - Best Known (163, 163+68, s)-Nets in Base 4

Best Known (163, 163+68, s)-Nets in Base 4

(163, 163+68, 531)-Net over F₄ — Constructive and digital

Digital (163, 231, 531)-net over F₄, using

3 times m-reduction [i] based on digital (163, 234, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 78, 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]

(163, 163+68, 1015)-Net over F₄ — Digital

Digital (163, 231, 1015)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+68, 55539)-Net in Base 4 — Upper bound on s

There is no (163, 231, 55540)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 911169 067200 457193 162485 452580 266910 896904 334535 748012 989985 446526 040059 682135 042183 178326 506983 613680 139868 588195 784386 792823 980337 512255 > 4²³¹ [i]