MinT - Best Known (112−76, 112, s)-Nets in Base 8

Best Known (112−76, 112, s)-Nets in Base 8

(112−76, 112, 65)-Net over F₈ — Constructive and digital

Digital (36, 112, 65)-net over F₈, using

t-expansion [i] based on digital (14, 112, 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]

(112−76, 112, 112)-Net over F₈ — Digital

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

t-expansion [i] based on digital (35, 112, 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]

(112−76, 112, 961)-Net in Base 8 — Upper bound on s

There is no (36, 112, 962)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 144009 755298 772438 051885 622552 316597 032819 462497 054293 209053 066430 280319 158534 835009 112624 393609 189088 > 8¹¹² [i]