MinT - Best Known (165, 165+83, s)-Nets in Base 4

Best Known (165, 165+83, s)-Nets in Base 4

(165, 165+83, 450)-Net over F₄ — Constructive and digital

Digital (165, 248, 450)-net over F₄, using

2 times m-reduction [i] based on digital (165, 250, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 125, 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]

(165, 165+83, 655)-Net over F₄ — Digital

Digital (165, 248, 655)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+83, 22761)-Net in Base 4 — Upper bound on s

There is no (165, 248, 22762)-net in base 4, because

1 times m-reduction [i] would yield (165, 247, 22762)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51223 807161 342242 236021 673038 366598 155524 375055 374009 628999 906947 207495 411352 012294 068131 860216 611899 677162 415088 205587 083993 242336 549007 688338 220805 > 4²⁴⁷ [i]