MinT - Best Known (54−41, 54, s)-Nets in Base 8

Best Known (54−41, 54, s)-Nets in Base 8

(54−41, 54, 48)-Net over F₈ — Constructive and digital

Digital (13, 54, 48)-net over F₈, using

t-expansion [i] based on digital (11, 54, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(54−41, 54, 56)-Net over F₈ — Digital

Digital (13, 54, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(54−41, 54, 281)-Net in Base 8 — Upper bound on s

There is no (13, 54, 282)-net in base 8, because

1 times m-reduction [i] would yield (13, 53, 282)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 773795 877764 232527 155214 071707 985012 272249 385322 > 8⁵³ [i]