MinT - Best Known (110−77, 110, s)-Nets in Base 8

Best Known (110−77, 110, s)-Nets in Base 8

(110−77, 110, 65)-Net over F₈ — Constructive and digital

Digital (33, 110, 65)-net over F₈, using

t-expansion [i] based on digital (14, 110, 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]

(110−77, 110, 97)-Net over F₈ — Digital

Digital (33, 110, 97)-net over F₈, using

t-expansion [i] based on digital (28, 110, 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]

(110−77, 110, 812)-Net in Base 8 — Upper bound on s

There is no (33, 110, 813)-net in base 8, because

1 times m-reduction [i] would yield (33, 109, 813)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 283 981695 131228 046250 250922 182224 829605 932790 885815 519696 426124 700548 034861 330242 933694 524204 407244 > 8¹⁰⁹ [i]