MinT - Best Known (168−131, 168, s)-Nets in Base 8

Best Known (168−131, 168, s)-Nets in Base 8

(168−131, 168, 98)-Net over F₈ — Constructive and digital

Digital (37, 168, 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]

(168−131, 168, 121)-Net over F₈ — Digital

Digital (37, 168, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(168−131, 168, 707)-Net in Base 8 — Upper bound on s

There is no (37, 168, 708)-net in base 8, because

1 times m-reduction [i] would yield (37, 167, 708)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 946322 334153 597557 287749 887123 983760 798897 613529 776709 411207 133198 838811 097245 194567 388523 768645 034669 073296 711739 330713 616496 362083 412130 767546 380587 > 8¹⁶⁷ [i]