MinT - Best Known (109−77, 109, s)-Nets in Base 8

Best Known (109−77, 109, s)-Nets in Base 8

(109−77, 109, 65)-Net over F₈ — Constructive and digital

Digital (32, 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]

(109−77, 109, 97)-Net over F₈ — Digital

Digital (32, 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]

(109−77, 109, 767)-Net in Base 8 — Upper bound on s

There is no (32, 109, 768)-net in base 8, because

1 times m-reduction [i] would yield (32, 108, 768)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 34 731737 920901 789967 062371 433484 443501 798916 185279 611918 289671 110010 938298 602295 321203 631895 408121 > 8¹⁰⁸ [i]