MinT - Best Known (129−91, 129, s)-Nets in Base 8

Best Known (129−91, 129, s)-Nets in Base 8

(129−91, 129, 98)-Net over F₈ — Constructive and digital

Digital (38, 129, 98)-net over F₈, using

t-expansion [i] based on digital (37, 129, 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]

(129−91, 129, 129)-Net over F₈ — Digital

Digital (38, 129, 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]

(129−91, 129, 904)-Net in Base 8 — Upper bound on s

There is no (38, 129, 905)-net in base 8, because

1 times m-reduction [i] would yield (38, 128, 905)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 39 792326 663686 960083 954274 409198 671351 647289 674448 298389 880180 682824 959052 874634 940590 463924 664459 914796 591442 092160 > 8¹²⁸ [i]