MinT - Best Known (58−33, 58, s)-Nets in Base 8

Best Known (58−33, 58, s)-Nets in Base 8

(58−33, 58, 65)-Net over F₈ — Constructive and digital

Digital (25, 58, 65)-net over F₈, using

t-expansion [i] based on digital (14, 58, 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]

(58−33, 58, 86)-Net over F₈ — Digital

Digital (25, 58, 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]

(58−33, 58, 1592)-Net in Base 8 — Upper bound on s

There is no (25, 58, 1593)-net in base 8, because

1 times m-reduction [i] would yield (25, 57, 1593)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3012 138344 293339 009772 736361 732400 048771 403586 480105 > 8⁵⁷ [i]