MinT - Best Known (133−93, 133, s)-Nets in Base 8

Best Known (133−93, 133, s)-Nets in Base 8

(133−93, 133, 98)-Net over F₈ — Constructive and digital

Digital (40, 133, 98)-net over F₈, using

t-expansion [i] based on digital (37, 133, 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]

(133−93, 133, 129)-Net over F₈ — Digital

Digital (40, 133, 129)-net over F₈, using

t-expansion [i] based on digital (38, 133, 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]

(133−93, 133, 974)-Net in Base 8 — Upper bound on s

There is no (40, 133, 975)-net in base 8, because

1 times m-reduction [i] would yield (40, 132, 975)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 162209 704714 430432 143221 103606 109804 665251 019238 860392 217927 723673 070153 430573 574606 254437 462805 725040 601851 320097 109234 > 8¹³² [i]