MinT - Best Known (67, 67+59, s)-Nets in Base 4

Best Known (67, 67+59, s)-Nets in Base 4

(67, 67+59, 90)-Net over F₄ — Constructive and digital

Digital (67, 126, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 63, 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]

(67, 67+59, 119)-Net over F₄ — Digital

Digital (67, 126, 119)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+59, 1507)-Net in Base 4 — Upper bound on s

There is no (67, 126, 1508)-net in base 4, because

1 times m-reduction [i] would yield (67, 125, 1508)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1813 818035 310302 689761 892228 509405 665374 634158 586359 776592 423686 949365 370264 > 4¹²⁵ [i]