MinT - Best Known (140−96, 140, s)-Nets in Base 8

Best Known (140−96, 140, s)-Nets in Base 8

(140−96, 140, 98)-Net over F₈ — Constructive and digital

Digital (44, 140, 98)-net over F₈, using

t-expansion [i] based on digital (37, 140, 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]

(140−96, 140, 130)-Net over F₈ — Digital

Digital (44, 140, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(140−96, 140, 1122)-Net in Base 8 — Upper bound on s

There is no (44, 140, 1123)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 758779 845373 779815 147532 813073 786356 759976 818559 047999 379883 957496 261308 327494 358251 743330 481220 661325 512359 667160 379294 144316 > 8¹⁴⁰ [i]