MinT - Best Known (70−48, 70, s)-Nets in Base 8

Best Known (70−48, 70, s)-Nets in Base 8

(70−48, 70, 65)-Net over F₈ — Constructive and digital

Digital (22, 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]

(70−48, 70, 76)-Net over F₈ — Digital

Digital (22, 70, 76)-net over F₈, using

t-expansion [i] based on digital (20, 70, 76)-net over F₈, using
- net from sequence [i] based on digital (20, 75)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
    - a curve from the manYPoints database [i]

(70−48, 70, 588)-Net in Base 8 — Upper bound on s

There is no (22, 70, 589)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1703 522403 740081 396369 031183 889074 726264 893149 109456 615611 049132 > 8⁷⁰ [i]