MinT - Best Known (25, 25+81, s)-Nets in Base 8

Best Known (25, 25+81, s)-Nets in Base 8

(25, 25+81, 65)-Net over F₈ — Constructive and digital

Digital (25, 106, 65)-net over F₈, using

t-expansion [i] based on digital (14, 106, 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]

(25, 25+81, 86)-Net over F₈ — Digital

Digital (25, 106, 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]

(25, 25+81, 503)-Net in Base 8 — Upper bound on s

There is no (25, 106, 504)-net in base 8, because

1 times m-reduction [i] would yield (25, 105, 504)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 66946 629284 965830 451952 058345 897807 485099 121305 764291 398926 188981 945598 554816 599206 320135 901346 > 8¹⁰⁵ [i]