MinT - Best Known (165, 165+73, s)-Nets in Base 4

Best Known (165, 165+73, s)-Nets in Base 4

(165, 165+73, 450)-Net over F₄ — Constructive and digital

Digital (165, 238, 450)-net over F₄, using

12 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+73, 880)-Net over F₄ — Digital

Digital (165, 238, 880)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+73, 43740)-Net in Base 4 — Upper bound on s

There is no (165, 238, 43741)-net in base 4, because

1 times m-reduction [i] would yield (165, 237, 43741)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48793 455225 811716 067250 063454 625363 680489 843214 764457 159863 932764 133831 294448 733152 418248 903211 276449 909961 733994 889036 479697 286606 502534 445450 > 4²³⁷ [i]