MinT - Best Known (50−22, 50, s)-Nets in Base 4

Best Known (50−22, 50, s)-Nets in Base 4

(50−22, 50, 76)-Net over F₄ — Constructive and digital

Digital (28, 50, 76)-net over F₄, using

trace code for nets [i] based on digital (3, 25, 38)-net over F₁₆, using
- net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
    - a function field by SÃ©mirat [i]

(50−22, 50, 883)-Net in Base 4 — Upper bound on s

There is no (28, 50, 884)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 272286 335498 940866 476526 339550 > 4⁵⁰ [i]