MinT - Best Known (253−79, 253, s)-Nets in Base 4

Best Known (253−79, 253, s)-Nets in Base 4

(253−79, 253, 450)-Net over F₄ — Constructive and digital

Digital (174, 253, 450)-net over F₄, using

t-expansion [i] based on digital (170, 253, 450)-net over F₄, using
- 7 times m-reduction [i] based on digital (170, 260, 450)-net over F₄, using
  - trace code for nets [i] based on digital (40, 130, 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]

(253−79, 253, 865)-Net over F₄ — Digital

Digital (174, 253, 865)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(253−79, 253, 39828)-Net in Base 4 — Upper bound on s

There is no (174, 253, 39829)-net in base 4, because

1 times m-reduction [i] would yield (174, 252, 39829)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 422662 247246 199066 771471 444212 290796 859311 871050 061190 008873 603926 131287 477047 888039 667946 105036 302198 622779 540664 528612 927327 992503 554981 392788 020032 > 4²⁵² [i]