MinT - Best Known (40, 40+45, s)-Nets in Base 8

Best Known (40, 40+45, s)-Nets in Base 8

(40, 40+45, 98)-Net over F₈ — Constructive and digital

Digital (40, 85, 98)-net over F₈, using

t-expansion [i] based on digital (37, 85, 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]

(40, 40+45, 129)-Net over F₈ — Digital

Digital (40, 85, 129)-net over F₈, using

t-expansion [i] based on digital (38, 85, 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]

(40, 40+45, 3616)-Net in Base 8 — Upper bound on s

There is no (40, 85, 3617)-net in base 8, because

1 times m-reduction [i] would yield (40, 84, 3617)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 7260 826935 783665 900662 875811 564637 235409 232640 107615 407389 357425 910670 852848 > 8⁸⁴ [i]