MinT - Best Known (39, 39+31, s)-Nets in Base 4

Best Known (39, 39+31, s)-Nets in Base 4

(39, 39+31, 90)-Net over F₄ — Constructive and digital

Digital (39, 70, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 35, 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]

(39, 39+31, 1247)-Net in Base 4 — Upper bound on s

There is no (39, 70, 1248)-net in base 4, because

1 times m-reduction [i] would yield (39, 69, 1248)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 351276 160709 992252 063784 165852 872876 174981 > 4⁶⁹ [i]