MinT - Best Known (235−75, 235, s)-Nets in Base 4

Best Known (235−75, 235, s)-Nets in Base 4

(235−75, 235, 450)-Net over F₄ — Constructive and digital

Digital (160, 235, 450)-net over F₄, using

5 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]

(235−75, 235, 745)-Net over F₄ — Digital

Digital (160, 235, 745)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(235−75, 235, 31332)-Net in Base 4 — Upper bound on s

There is no (160, 235, 31333)-net in base 4, because

1 times m-reduction [i] would yield (160, 234, 31333)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 762 720991 168482 900969 332067 477710 306978 801339 309642 719336 651039 700208 342163 386728 002562 590684 423708 104543 274380 482084 093851 436564 234734 822060 > 4²³⁴ [i]