MinT - Best Known (31, 31+45, s)-Nets in Base 8

Best Known (31, 31+45, s)-Nets in Base 8

(31, 31+45, 65)-Net over F₈ — Constructive and digital

Digital (31, 76, 65)-net over F₈, using

t-expansion [i] based on digital (14, 76, 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]

(31, 31+45, 97)-Net over F₈ — Digital

Digital (31, 76, 97)-net over F₈, using

t-expansion [i] based on digital (28, 76, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(31, 31+45, 1536)-Net in Base 8 — Upper bound on s

There is no (31, 76, 1537)-net in base 8, because

1 times m-reduction [i] would yield (31, 75, 1537)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 54 003324 615440 767774 265798 848518 413714 526975 970196 768222 795415 643904 > 8⁷⁵ [i]