MinT - Best Known (54, 54+39, s)-Nets in Base 3

Best Known (54, 54+39, s)-Nets in Base 3

(54, 54+39, 72)-Net over F₃ — Constructive and digital

Digital (54, 93, 72)-net over F₃, using

1 times m-reduction [i] based on 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, 54+39, 87)-Net over F₃ — Digital

Digital (54, 93, 87)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+39, 791)-Net in Base 3 — Upper bound on s

There is no (54, 93, 792)-net in base 3, because

1 times m-reduction [i] would yield (54, 92, 792)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79 251000 758656 460025 051077 561570 772227 723745 > 3⁹² [i]