MinT - Best Known (54, 54+46, s)-Nets in Base 4

Best Known (54, 54+46, s)-Nets in Base 4

(54, 54+46, 90)-Net over F₄ — Constructive and digital

Digital (54, 100, 90)-net over F₄, using

trace code for nets [i] based on digital (4, 50, 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]

(54, 54+46, 105)-Net over F₄ — Digital

Digital (54, 100, 105)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+46, 1284)-Net in Base 4 — Upper bound on s

There is no (54, 100, 1285)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 619350 692815 688511 732721 780916 424344 770759 814261 814623 587584 > 4¹⁰⁰ [i]