MinT - Best Known (140−99, 140, s)-Nets in Base 8

Best Known (140−99, 140, s)-Nets in Base 8

(140−99, 140, 98)-Net over F₈ — Constructive and digital

Digital (41, 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]

(140−99, 140, 129)-Net over F₈ — Digital

Digital (41, 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]

(140−99, 140, 964)-Net in Base 8 — Upper bound on s

There is no (41, 140, 965)-net in base 8, because

1 times m-reduction [i] would yield (41, 139, 965)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 342153 624972 401544 979704 622752 774674 183096 705843 417003 707015 836917 989958 972719 086874 117780 881407 965445 146617 270210 138285 865296 > 8¹³⁹ [i]