MinT - Best Known (156, 156+69, s)-Nets in Base 4

Best Known (156, 156+69, s)-Nets in Base 4

(156, 156+69, 450)-Net over F₄ — Constructive and digital

Digital (156, 225, 450)-net over F₄, using

7 times m-reduction [i] based on digital (156, 232, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 116, 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]

(156, 156+69, 839)-Net over F₄ — Digital

Digital (156, 225, 839)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+69, 41742)-Net in Base 4 — Upper bound on s

There is no (156, 225, 41743)-net in base 4, because

1 times m-reduction [i] would yield (156, 224, 41743)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 727 180602 785698 788729 189310 367659 710692 660015 247518 750090 713369 154394 950937 423866 885747 088973 475298 203129 524623 767386 423676 276571 445528 > 4²²⁴ [i]