MinT - Best Known (36, 36+54, s)-Nets in Base 8

Best Known (36, 36+54, s)-Nets in Base 8

(36, 36+54, 65)-Net over F₈ — Constructive and digital

Digital (36, 90, 65)-net over F₈, using

t-expansion [i] based on digital (14, 90, 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]

(36, 36+54, 112)-Net over F₈ — Digital

Digital (36, 90, 112)-net over F₈, using

t-expansion [i] based on digital (35, 90, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(36, 36+54, 1581)-Net in Base 8 — Upper bound on s

There is no (36, 90, 1582)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1919 220491 147322 331695 821907 156300 840460 255794 778371 233333 992418 160711 442549 364004 > 8⁹⁰ [i]