MinT - Best Known (40, 40+72, s)-Nets in Base 8

Best Known (40, 40+72, s)-Nets in Base 8

(40, 40+72, 98)-Net over F₈ — Constructive and digital

Digital (40, 112, 98)-net over F₈, using

t-expansion [i] based on digital (37, 112, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(40, 40+72, 129)-Net over F₈ — Digital

Digital (40, 112, 129)-net over F₈, using

t-expansion [i] based on digital (38, 112, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(40, 40+72, 1293)-Net in Base 8 — Upper bound on s

There is no (40, 112, 1294)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 142048 766851 717062 968104 113470 847247 943120 257823 940292 142992 746761 399428 592248 619677 309872 919705 909480 > 8¹¹² [i]