MinT - Best Known (81−55, 81, s)-Nets in Base 8

Best Known (81−55, 81, s)-Nets in Base 8

(81−55, 81, 65)-Net over F₈ — Constructive and digital

Digital (26, 81, 65)-net over F₈, using

t-expansion [i] based on digital (14, 81, 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]

(81−55, 81, 86)-Net over F₈ — Digital

Digital (26, 81, 86)-net over F₈, using

t-expansion [i] based on digital (25, 81, 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]

(81−55, 81, 723)-Net in Base 8 — Upper bound on s

There is no (26, 81, 724)-net in base 8, because

1 times m-reduction [i] would yield (26, 80, 724)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 826584 015185 032221 231479 865679 168643 644593 465420 489173 842860 597310 740648 > 8⁸⁰ [i]