MinT - Best Known (145−105, 145, s)-Nets in Base 8

Best Known (145−105, 145, s)-Nets in Base 8

(145−105, 145, 98)-Net over F₈ — Constructive and digital

Digital (40, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(145−105, 145, 129)-Net over F₈ — Digital

Digital (40, 145, 129)-net over F₈, using

t-expansion [i] based on digital (38, 145, 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]

(145−105, 145, 882)-Net in Base 8 — Upper bound on s

There is no (40, 145, 883)-net in base 8, because

1 times m-reduction [i] would yield (40, 144, 883)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11130 655825 152816 936948 011566 558624 515302 938477 791377 263489 339662 986388 839693 986160 958970 204074 120517 890719 444263 088920 680875 885168 > 8¹⁴⁴ [i]