MinT - Best Known (50−30, 50, s)-Nets in Base 8

Best Known (50−30, 50, s)-Nets in Base 8

(50−30, 50, 65)-Net over F₈ — Constructive and digital

Digital (20, 50, 65)-net over F₈, using

t-expansion [i] based on digital (14, 50, 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]

(50−30, 50, 76)-Net over F₈ — Digital

Digital (20, 50, 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]

(50−30, 50, 930)-Net in Base 8 — Upper bound on s

There is no (20, 50, 931)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1437 753211 149850 956009 951753 593144 036187 554976 > 8⁵⁰ [i]