MinT - Best Known (39, 39+101, s)-Nets in Base 8

Best Known (39, 39+101, s)-Nets in Base 8

(39, 39+101, 98)-Net over F₈ — Constructive and digital

Digital (39, 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]

(39, 39+101, 129)-Net over F₈ — Digital

Digital (39, 140, 129)-net over F₈, using

t-expansion [i] based on digital (38, 140, 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]

(39, 39+101, 870)-Net in Base 8 — Upper bound on s

There is no (39, 140, 871)-net in base 8, because

1 times m-reduction [i] would yield (39, 139, 871)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 346443 672113 119089 622869 189499 565300 482153 721389 996848 147271 273278 831693 097429 765847 790151 485460 043046 434129 497737 224349 596836 > 8¹³⁹ [i]