MinT - Best Known (57−31, 57, s)-Nets in Base 8

Best Known (57−31, 57, s)-Nets in Base 8

(57−31, 57, 65)-Net over F₈ — Constructive and digital

Digital (26, 57, 65)-net over F₈, using

t-expansion [i] based on digital (14, 57, 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]

(57−31, 57, 86)-Net over F₈ — Digital

Digital (26, 57, 86)-net over F₈, using

t-expansion [i] based on digital (25, 57, 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]

(57−31, 57, 2149)-Net in Base 8 — Upper bound on s

There is no (26, 57, 2150)-net in base 8, because

1 times m-reduction [i] would yield (26, 56, 2150)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 375 106613 476015 269078 585584 128240 144604 304279 459216 > 8⁵⁶ [i]