MinT - Best Known (236−75, 236, s)-Nets in Base 4

Best Known (236−75, 236, s)-Nets in Base 4

(236−75, 236, 450)-Net over F₄ — Constructive and digital

Digital (161, 236, 450)-net over F₄, using

6 times m-reduction [i] based on digital (161, 242, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 121, 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]

(236−75, 236, 760)-Net over F₄ — Digital

Digital (161, 236, 760)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(236−75, 236, 32529)-Net in Base 4 — Upper bound on s

There is no (161, 236, 32530)-net in base 4, because

1 times m-reduction [i] would yield (161, 235, 32530)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3049 519174 597199 177812 794630 797416 839713 595064 054862 082057 576437 788897 031565 170287 653421 007422 519860 441011 617301 893570 373500 665559 739815 466272 > 4²³⁵ [i]