MinT - Best Known (40, 156, s)-Nets in Base 8

Best Known (40, 156, s)-Nets in Base 8

(40, 156, 98)-Net over F₈ — Constructive and digital

Digital (40, 156, 98)-net over F₈, using

t-expansion [i] based on digital (37, 156, 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, 156, 129)-Net over F₈ — Digital

Digital (40, 156, 129)-net over F₈, using

t-expansion [i] based on digital (38, 156, 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, 156, 824)-Net in Base 8 — Upper bound on s

There is no (40, 156, 825)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 765 600415 235491 951575 576784 729868 793758 418173 872382 286173 811071 654015 773723 218122 108872 990012 544946 808407 372011 238085 018688 584340 446385 099712 > 8¹⁵⁶ [i]