MinT - Best Known (168−125, 168, s)-Nets in Base 8

Best Known (168−125, 168, s)-Nets in Base 8

(168−125, 168, 98)-Net over F₈ — Constructive and digital

Digital (43, 168, 98)-net over F₈, using

t-expansion [i] based on 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]

(168−125, 168, 129)-Net over F₈ — Digital

Digital (43, 168, 129)-net over F₈, using

t-expansion [i] based on digital (38, 168, 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]

(168−125, 168, 886)-Net in Base 8 — Upper bound on s

There is no (43, 168, 887)-net in base 8, because

1 times m-reduction [i] would yield (43, 167, 887)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 667793 179460 013424 137930 365369 250995 637388 061859 969602 508812 429023 018670 763328 826799 433878 646016 675807 590878 277928 504246 648445 891867 647971 119610 721608 > 8¹⁶⁷ [i]