MinT - Best Known (34, 34+72, s)-Nets in Base 8

Best Known (34, 34+72, s)-Nets in Base 8

(34, 34+72, 65)-Net over F₈ — Constructive and digital

Digital (34, 106, 65)-net over F₈, using

t-expansion [i] based on digital (14, 106, 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]

(34, 34+72, 98)-Net over F₈ — Digital

Digital (34, 106, 98)-net over F₈, using

net from sequence [i] based on digital (34, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 34 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(34, 34+72, 908)-Net in Base 8 — Upper bound on s

There is no (34, 106, 909)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 553576 561686 166163 653814 362975 439311 692496 763216 133535 015529 408916 932243 907125 699937 782333 551020 > 8¹⁰⁶ [i]