MinT - Best Known (38−15, 38, s)-Nets in Base 4

Best Known (38−15, 38, s)-Nets in Base 4

(38−15, 38, 90)-Net over F₄ — Constructive and digital

Digital (23, 38, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 19, 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]

(38−15, 38, 1709)-Net in Base 4 — Upper bound on s

There is no (23, 38, 1710)-net in base 4, because

1 times m-reduction [i] would yield (23, 37, 1710)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 18960 345311 008581 312652 > 4³⁷ [i]