MinT - Best Known (252−86, 252, s)-Nets in Base 4

Best Known (252−86, 252, s)-Nets in Base 4

(252−86, 252, 450)-Net over F₄ — Constructive and digital

Digital (166, 252, 450)-net over F₄, using

trace code for nets [i] based on digital (40, 126, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(252−86, 252, 620)-Net over F₄ — Digital

Digital (166, 252, 620)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(252−86, 252, 18962)-Net in Base 4 — Upper bound on s

There is no (166, 252, 18963)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 457694 432793 189940 429485 503778 364497 669452 040326 805810 047536 719900 951887 388018 914415 850460 018836 872605 303453 933508 520053 210073 417621 274486 852270 528640 > 4²⁵² [i]