MinT - Best Known (41, 41+108, s)-Nets in Base 8

Best Known (41, 41+108, s)-Nets in Base 8

(41, 41+108, 98)-Net over F₈ — Constructive and digital

Digital (41, 149, 98)-net over F₈, using

t-expansion [i] based on digital (37, 149, 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]

(41, 41+108, 129)-Net over F₈ — Digital

Digital (41, 149, 129)-net over F₈, using

t-expansion [i] based on digital (38, 149, 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]

(41, 41+108, 895)-Net in Base 8 — Upper bound on s

There is no (41, 149, 896)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 368 108339 674508 573155 162039 615389 063920 561668 401481 360492 796223 818769 200926 310558 160670 233404 774321 359698 696813 913332 592668 692932 373749 > 8¹⁴⁹ [i]