MinT - Best Known (31, 31+78, s)-Nets in Base 8

Best Known (31, 31+78, s)-Nets in Base 8

(31, 31+78, 65)-Net over F₈ — Constructive and digital

Digital (31, 109, 65)-net over F₈, using

t-expansion [i] based on digital (14, 109, 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+78, 97)-Net over F₈ — Digital

Digital (31, 109, 97)-net over F₈, using

t-expansion [i] based on digital (28, 109, 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+78, 710)-Net in Base 8 — Upper bound on s

There is no (31, 109, 711)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 276 639650 083040 595299 426757 371383 068961 017241 331950 640770 472457 794690 854493 688121 820775 573977 755568 > 8¹⁰⁹ [i]