MinT - Best Known (41, 41+33, s)-Nets in Base 4

Best Known (41, 41+33, s)-Nets in Base 4

(41, 41+33, 90)-Net over F₄ — Constructive and digital

Digital (41, 74, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 37, 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]

(41, 41+33, 92)-Net over F₄ — Digital

Digital (41, 74, 92)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+33, 1252)-Net in Base 4 — Upper bound on s

There is no (41, 74, 1253)-net in base 4, because

1 times m-reduction [i] would yield (41, 73, 1253)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 89 344733 131808 386433 769782 175068 047289 826130 > 4⁷³ [i]