MinT - Best Known (237−77, 237, s)-Nets in Base 4

Best Known (237−77, 237, s)-Nets in Base 4

(237−77, 237, 450)-Net over F₄ — Constructive and digital

Digital (160, 237, 450)-net over F₄, using

3 times m-reduction [i] based on digital (160, 240, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 120, 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]

(237−77, 237, 702)-Net over F₄ — Digital

Digital (160, 237, 702)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−77, 237, 27434)-Net in Base 4 — Upper bound on s

There is no (160, 237, 27435)-net in base 4, because

1 times m-reduction [i] would yield (160, 236, 27435)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12201 269064 423417 568882 577935 895627 330029 522339 393519 789302 551354 207408 926705 567698 772513 953077 744007 751820 450039 449590 403410 229180 987966 187770 > 4²³⁶ [i]