MinT - Best Known (86−47, 86, s)-Nets in Base 8

Best Known (86−47, 86, s)-Nets in Base 8

(86−47, 86, 98)-Net over F₈ — Constructive and digital

Digital (39, 86, 98)-net over F₈, using

t-expansion [i] based on digital (37, 86, 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]

(86−47, 86, 129)-Net over F₈ — Digital

Digital (39, 86, 129)-net over F₈, using

t-expansion [i] based on digital (38, 86, 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]

(86−47, 86, 2915)-Net in Base 8 — Upper bound on s

There is no (39, 86, 2916)-net in base 8, because

1 times m-reduction [i] would yield (39, 85, 2916)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 58025 147605 689999 521396 168362 766909 490023 146660 686208 735618 753921 860908 744536 > 8⁸⁵ [i]