MinT - Best Known (159−115, 159, s)-Nets in Base 8

Best Known (159−115, 159, s)-Nets in Base 8

(159−115, 159, 98)-Net over F₈ — Constructive and digital

Digital (44, 159, 98)-net over F₈, using

t-expansion [i] based on digital (37, 159, 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]

(159−115, 159, 130)-Net over F₈ — Digital

Digital (44, 159, 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]

(159−115, 159, 969)-Net in Base 8 — Upper bound on s

There is no (44, 159, 970)-net in base 8, because

1 times m-reduction [i] would yield (44, 158, 970)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 50687 697789 801077 473861 482465 934316 872008 042466 016883 647470 253606 452824 825285 159758 724795 122436 699756 041777 351424 823329 890503 041919 223905 895428 > 8¹⁵⁸ [i]