MinT - Best Known (61−35, 61, s)-Nets in Base 8

Best Known (61−35, 61, s)-Nets in Base 8

(61−35, 61, 65)-Net over F₈ — Constructive and digital

Digital (26, 61, 65)-net over F₈, using

t-expansion [i] based on digital (14, 61, 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]

(61−35, 61, 86)-Net over F₈ — Digital

Digital (26, 61, 86)-net over F₈, using

t-expansion [i] based on digital (25, 61, 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]

(61−35, 61, 1568)-Net in Base 8 — Upper bound on s

There is no (26, 61, 1569)-net in base 8, because

1 times m-reduction [i] would yield (26, 60, 1569)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 548806 022881 586604 001086 719478 540959 476900 412610 250960 > 8⁶⁰ [i]