MinT - Best Known (51−30, 51, s)-Nets in Base 8

Best Known (51−30, 51, s)-Nets in Base 8

(51−30, 51, 65)-Net over F₈ — Constructive and digital

Digital (21, 51, 65)-net over F₈, using

t-expansion [i] based on digital (14, 51, 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]

(51−30, 51, 76)-Net over F₈ — Digital

Digital (21, 51, 76)-net over F₈, using

t-expansion [i] based on digital (20, 51, 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]

(51−30, 51, 1070)-Net in Base 8 — Upper bound on s

There is no (21, 51, 1071)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11535 637841 016570 664745 953749 938302 926361 693176 > 8⁵¹ [i]