MinT - Best Known (147, 147+65, s)-Nets in Base 4

Best Known (147, 147+65, s)-Nets in Base 4

(147, 147+65, 450)-Net over F₄ — Constructive and digital

Digital (147, 212, 450)-net over F₄, using

2 times m-reduction [i] based on digital (147, 214, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 107, 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]

(147, 147+65, 798)-Net over F₄ — Digital

Digital (147, 212, 798)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(147, 147+65, 39747)-Net in Base 4 — Upper bound on s

There is no (147, 212, 39748)-net in base 4, because

1 times m-reduction [i] would yield (147, 211, 39748)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 837795 435977 531433 905983 751699 556670 977102 114258 053532 859714 825844 371377 266637 002846 434301 160861 256811 427176 509759 610462 710158 > 4²¹¹ [i]