MinT - Best Known (54, 54+38, s)-Nets in Base 3

Best Known (54, 54+38, s)-Nets in Base 3

(54, 54+38, 80)-Net over F₃ — Constructive and digital

Digital (54, 92, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 46, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(54, 54+38, 90)-Net over F₃ — Digital

Digital (54, 92, 90)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+38, 791)-Net in Base 3 — Upper bound on s

There is no (54, 92, 792)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79 251000 758656 460025 051077 561570 772227 723745 > 3⁹² [i]