MinT - Best Known (232−71, 232, s)-Nets in Base 4

Best Known (232−71, 232, s)-Nets in Base 4

(232−71, 232, 450)-Net over F₄ — Constructive and digital

Digital (161, 232, 450)-net over F₄, using

10 times m-reduction [i] based on digital (161, 242, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 121, 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]

(232−71, 232, 869)-Net over F₄ — Digital

Digital (161, 232, 869)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−71, 232, 43596)-Net in Base 4 — Upper bound on s

There is no (161, 232, 43597)-net in base 4, because

1 times m-reduction [i] would yield (161, 231, 43597)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 911910 805818 878412 448348 063214 921410 217871 303935 687372 078297 173113 184994 998545 123919 029857 426294 391674 934869 913558 826587 939455 778084 831848 > 4²³¹ [i]