MinT - Best Known (45−33, 45, s)-Nets in Base 8

Best Known (45−33, 45, s)-Nets in Base 8

(45−33, 45, 48)-Net over F₈ — Constructive and digital

Digital (12, 45, 48)-net over F₈, using

t-expansion [i] based on digital (11, 45, 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]

(45−33, 45, 49)-Net over F₈ — Digital

Digital (12, 45, 49)-net over F₈, using

net from sequence [i] based on digital (12, 48)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 12 and N(F) ≥ 49, using
  - a curve from the manYPoints database [i]

(45−33, 45, 286)-Net in Base 8 — Upper bound on s

There is no (12, 45, 287)-net in base 8, because

1 times m-reduction [i] would yield (12, 44, 287)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5723 772412 809379 909403 156094 215144 289315 > 8⁴⁴ [i]