MinT - Best Known (59−25, 59, s)-Nets in Base 4

Best Known (59−25, 59, s)-Nets in Base 4

(59−25, 59, 90)-Net over F₄ — Constructive and digital

Digital (34, 59, 90)-net over F₄, using

1 times m-reduction [i] based on digital (34, 60, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 30, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(59−25, 59, 92)-Net over F₄ — Digital

Digital (34, 59, 92)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(59−25, 59, 1423)-Net in Base 4 — Upper bound on s

There is no (34, 59, 1424)-net in base 4, because

1 times m-reduction [i] would yield (34, 58, 1424)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 83522 068287 255720 383969 999357 134615 > 4⁵⁸ [i]