MinT - Best Known (163, 163+73, s)-Nets in Base 4

Best Known (163, 163+73, s)-Nets in Base 4

(163, 163+73, 450)-Net over F₄ — Constructive and digital

Digital (163, 236, 450)-net over F₄, using

10 times m-reduction [i] based on digital (163, 246, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 123, 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]

(163, 163+73, 845)-Net over F₄ — Digital

Digital (163, 236, 845)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+73, 40496)-Net in Base 4 — Upper bound on s

There is no (163, 236, 40497)-net in base 4, because

1 times m-reduction [i] would yield (163, 235, 40497)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3050 945017 363769 815361 950107 102724 858016 477273 747542 311533 032300 492775 246951 233187 628638 221676 979125 516565 495225 458088 439442 646659 900552 096452 > 4²³⁵ [i]