MinT - Best Known (162, 162+74, s)-Nets in Base 4

Best Known (162, 162+74, s)-Nets in Base 4

(162, 162+74, 450)-Net over F₄ — Constructive and digital

Digital (162, 236, 450)-net over F₄, using

8 times m-reduction [i] based on digital (162, 244, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 122, 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]

(162, 162+74, 801)-Net over F₄ — Digital

Digital (162, 236, 801)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(162, 162+74, 33772)-Net in Base 4 — Upper bound on s

There is no (162, 236, 33773)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12196 834351 528624 413690 040985 759863 734678 019999 685510 129718 819215 130154 699525 738467 054332 856977 571054 564891 429969 585961 941162 546728 450478 034732 > 4²³⁶ [i]