MinT - Best Known (40−16, 40, s)-Nets in Base 4

Best Known (40−16, 40, s)-Nets in Base 4

(40−16, 40, 90)-Net over F₄ — Constructive and digital

Digital (24, 40, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 20, 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]

(40−16, 40, 1278)-Net in Base 4 — Upper bound on s

There is no (24, 40, 1279)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 210858 804365 526024 025353 > 4⁴⁰ [i]