MinT - Best Known (44−24, 44, s)-Nets in Base 8

Best Known (44−24, 44, s)-Nets in Base 8

(44−24, 44, 65)-Net over F₈ — Constructive and digital

Digital (20, 44, 65)-net over F₈, using

t-expansion [i] based on digital (14, 44, 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]

(44−24, 44, 76)-Net over F₈ — Digital

Digital (20, 44, 76)-net over F₈, using

net from sequence [i] based on digital (20, 75)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
  - a curve from the manYPoints database [i]

(44−24, 44, 1540)-Net in Base 8 — Upper bound on s

There is no (20, 44, 1541)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5479 943021 994860 608344 069474 893404 466368 > 8⁴⁴ [i]