MinT - Best Known (54, 94, s)-Nets in Base 3

Best Known (54, 94, s)-Nets in Base 3

(54, 94, 72)-Net over F₃ — Constructive and digital

Digital (54, 94, 72)-net over F₃, using

trace code for nets [i] based on digital (7, 47, 36)-net over F₉, using
- net from sequence [i] based on digital (7, 35)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
    - a function field by SÃ©mirat [i]

(54, 94, 85)-Net over F₃ — Digital

Digital (54, 94, 85)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 94, 706)-Net in Base 3 — Upper bound on s

There is no (54, 94, 707)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 718 795986 233356 004421 350257 183788 032600 937657 > 3⁹⁴ [i]