MinT - Best Known (50−24, 50, s)-Nets in Base 4

Best Known (50−24, 50, s)-Nets in Base 4

(50−24, 50, 48)-Net over F₄ — Constructive and digital

Digital (26, 50, 48)-net over F₄, using

trace code for nets [i] based on digital (1, 25, 24)-net over F₁₆, using
- net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, using
    - a function field by SÃ©mirat [i]

(50−24, 50, 55)-Net over F₄ — Digital

Digital (26, 50, 55)-net over F₄, using

net from sequence [i] based on digital (26, 54)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 26 and N(F) ≥ 55, using
  - Drinfeld modules of rank 1 [i]

(50−24, 50, 559)-Net in Base 4 — Upper bound on s

There is no (26, 50, 560)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 289674 726822 068926 111760 036115 > 4⁵⁰ [i]