MinT - Best Known (70−44, 70, s)-Nets in Base 8

Best Known (70−44, 70, s)-Nets in Base 8

(70−44, 70, 65)-Net over F₈ — Constructive and digital

Digital (26, 70, 65)-net over F₈, using

t-expansion [i] based on digital (14, 70, 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]

(70−44, 70, 86)-Net over F₈ — Digital

Digital (26, 70, 86)-net over F₈, using

t-expansion [i] based on digital (25, 70, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(70−44, 70, 952)-Net in Base 8 — Upper bound on s

There is no (26, 70, 953)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1646 854400 976537 599773 783636 271536 974961 584081 781892 236673 510652 > 8⁷⁰ [i]