MinT - Best Known (56−31, 56, s)-Nets in Base 8

Best Known (56−31, 56, s)-Nets in Base 8

(56−31, 56, 65)-Net over F₈ — Constructive and digital

Digital (25, 56, 65)-net over F₈, using

t-expansion [i] based on digital (14, 56, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(56−31, 56, 86)-Net over F₈ — Digital

Digital (25, 56, 86)-net over F₈, using

net from sequence [i] based on digital (25, 85)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(56−31, 56, 1870)-Net in Base 8 — Upper bound on s

There is no (25, 56, 1871)-net in base 8, because

1 times m-reduction [i] would yield (25, 55, 1871)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 47 074425 261229 649977 215793 068742 482205 420540 584056 > 8⁵⁵ [i]