MinT - Best Known (40−18, 40, s)-Nets in Base 4

Best Known (40−18, 40, s)-Nets in Base 4

(40−18, 40, 66)-Net over F₄ — Constructive and digital

Digital (22, 40, 66)-net over F₄, using

trace code for nets [i] based on digital (2, 20, 33)-net over F₁₆, using
- net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
    - a function field by SÃ©mirat [i]

(40−18, 40, 648)-Net in Base 4 — Upper bound on s

There is no (22, 40, 649)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 219798 390715 092548 480484 > 4⁴⁰ [i]