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

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

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

Digital (35, 96, 65)-net over F₈, using

t-expansion [i] based on digital (14, 96, 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]

(35, 35+61, 112)-Net over F₈ — Digital

Digital (35, 96, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(35, 35+61, 1227)-Net in Base 8 — Upper bound on s

There is no (35, 96, 1228)-net in base 8, because

1 times m-reduction [i] would yield (35, 95, 1228)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 63 406239 289652 393863 158730 954414 072685 279119 636528 270911 455968 083613 917142 707351 979728 > 8⁹⁵ [i]