MinT - Best Known (70−45, 70, s)-Nets in Base 8

Best Known (70−45, 70, s)-Nets in Base 8

(70−45, 70, 65)-Net over F₈ — Constructive and digital

Digital (25, 70, 65)-net over F₈, using

t-expansion [i] based on digital (14, 70, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(70−45, 70, 86)-Net over F₈ — Digital

Digital (25, 70, 86)-net over F₈, using

net from sequence [i] based on digital (25, 85)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(70−45, 70, 865)-Net in Base 8 — Upper bound on s

There is no (25, 70, 866)-net in base 8, because

1 times m-reduction [i] would yield (25, 69, 866)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 206 738262 645291 611901 310399 374942 965297 585729 913934 788005 818032 > 8⁶⁹ [i]