MinT - Best Known (255−86, 255, s)-Nets in Base 4

Best Known (255−86, 255, s)-Nets in Base 4

(255−86, 255, 450)-Net over F₄ — Constructive and digital

Digital (169, 255, 450)-net over F₄, using

3 times m-reduction [i] based on digital (169, 258, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 129, 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]

(255−86, 255, 654)-Net over F₄ — Digital

Digital (169, 255, 654)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(255−86, 255, 20891)-Net in Base 4 — Upper bound on s

There is no (169, 255, 20892)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3355 399645 690326 782534 180141 771852 634807 032113 225842 537349 955225 622454 168390 186326 985670 144051 280068 384925 796010 654649 656065 054011 193874 289013 883554 207084 > 4²⁵⁵ [i]