MinT - Best Known (227−70, 227, s)-Nets in Base 4

Best Known (227−70, 227, s)-Nets in Base 4

(227−70, 227, 450)-Net over F₄ — Constructive and digital

Digital (157, 227, 450)-net over F₄, using

7 times m-reduction [i] based on digital (157, 234, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 117, 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]

(227−70, 227, 827)-Net over F₄ — Digital

Digital (157, 227, 827)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(227−70, 227, 37204)-Net in Base 4 — Upper bound on s

There is no (157, 227, 37205)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46532 998055 451750 891526 018985 753274 063127 719849 496869 078794 210811 165157 216756 034982 472638 681788 953454 392812 737459 057947 083191 978746 489768 > 4²²⁷ [i]