MinT - Best Known (165, 165+71, s)-Nets in Base 4

Best Known (165, 165+71, s)-Nets in Base 4

(165, 165+71, 531)-Net over F₄ — Constructive and digital

Digital (165, 236, 531)-net over F₄, using

1 times m-reduction [i] based on digital (165, 237, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 79, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(165, 165+71, 945)-Net over F₄ — Digital

Digital (165, 236, 945)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+71, 51085)-Net in Base 4 — Upper bound on s

There is no (165, 236, 51086)-net in base 4, because

1 times m-reduction [i] would yield (165, 235, 51086)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3048 618540 695767 636654 103367 393903 974751 696267 996042 643872 929663 021169 633894 120050 951110 060042 792496 192640 315367 569167 478694 627580 648460 359464 > 4²³⁵ [i]