MinT - Best Known (141−101, 141, s)-Nets in Base 8

Best Known (141−101, 141, s)-Nets in Base 8

(141−101, 141, 98)-Net over F₈ — Constructive and digital

Digital (40, 141, 98)-net over F₈, using

t-expansion [i] based on digital (37, 141, 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]

(141−101, 141, 129)-Net over F₈ — Digital

Digital (40, 141, 129)-net over F₈, using

t-expansion [i] based on digital (38, 141, 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]

(141−101, 141, 908)-Net in Base 8 — Upper bound on s

There is no (40, 141, 909)-net in base 8, because

1 times m-reduction [i] would yield (40, 140, 909)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 727105 738883 436827 816342 612231 569383 991846 524467 830780 656744 810122 128601 077259 158939 629071 980733 602996 398573 980776 233921 103376 > 8¹⁴⁰ [i]