MinT - Best Known (39, 166, s)-Nets in Base 8

Best Known (39, 166, s)-Nets in Base 8

(39, 166, 98)-Net over F₈ — Constructive and digital

Digital (39, 166, 98)-net over F₈, using

t-expansion [i] based on digital (37, 166, 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]

(39, 166, 129)-Net over F₈ — Digital

Digital (39, 166, 129)-net over F₈, using

t-expansion [i] based on digital (38, 166, 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]

(39, 166, 765)-Net in Base 8 — Upper bound on s

There is no (39, 166, 766)-net in base 8, because

1 times m-reduction [i] would yield (39, 165, 766)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105450 847490 516765 885567 833776 578893 762268 391688 865499 468209 583684 714406 080410 710065 902759 163047 317788 283107 927507 248580 549442 801061 408093 658471 922656 > 8¹⁶⁵ [i]