MinT - Best Known (152, 152+69, s)-Nets in Base 4

Best Known (152, 152+69, s)-Nets in Base 4

(152, 152+69, 450)-Net over F₄ — Constructive and digital

Digital (152, 221, 450)-net over F₄, using

3 times m-reduction [i] based on digital (152, 224, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 112, 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]

(152, 152+69, 769)-Net over F₄ — Digital

Digital (152, 221, 769)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(152, 152+69, 35456)-Net in Base 4 — Upper bound on s

There is no (152, 221, 35457)-net in base 4, because

1 times m-reduction [i] would yield (152, 220, 35457)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 840591 227187 693933 711368 274706 955958 886021 561207 411655 291474 045944 556134 239372 561694 753827 676582 924841 107346 759483 157427 165900 287104 > 4²²⁰ [i]