MinT - Best Known (54, 54+43, s)-Nets in Base 5

Best Known (54, 54+43, s)-Nets in Base 5

(54, 54+43, 132)-Net over F₅ — Constructive and digital

Digital (54, 97, 132)-net over F₅, using

3 times m-reduction [i] based on digital (54, 100, 132)-net over F₅, using
- trace code for nets [i] based on digital (4, 50, 66)-net over F₂₅, using
  - net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
      - a function field by GarcÃa and Quoos [i]

(54, 54+43, 155)-Net over F₅ — Digital

Digital (54, 97, 155)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+43, 3386)-Net in Base 5 — Upper bound on s

There is no (54, 97, 3387)-net in base 5, because

1 times m-reduction [i] would yield (54, 96, 3387)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 12 645633 078009 411160 065941 313581 064572 676279 842671 652556 542576 122525 > 5⁹⁶ [i]