MinT - Best Known (116−85, 116, s)-Nets in Base 8

Best Known (116−85, 116, s)-Nets in Base 8

(116−85, 116, 65)-Net over F₈ — Constructive and digital

Digital (31, 116, 65)-net over F₈, using

t-expansion [i] based on digital (14, 116, 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]

(116−85, 116, 97)-Net over F₈ — Digital

Digital (31, 116, 97)-net over F₈, using

t-expansion [i] based on digital (28, 116, 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]

(116−85, 116, 674)-Net in Base 8 — Upper bound on s

There is no (31, 116, 675)-net in base 8, because

1 times m-reduction [i] would yield (31, 115, 675)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 74 436642 575875 797793 441634 666694 471039 097819 159994 737951 622308 784081 839206 291736 307182 153714 235812 791920 > 8¹¹⁵ [i]