MinT - Best Known (34−21, 34, s)-Nets in Base 8

Best Known (34−21, 34, s)-Nets in Base 8

(34−21, 34, 48)-Net over F₈ — Constructive and digital

Digital (13, 34, 48)-net over F₈, using

t-expansion [i] based on digital (11, 34, 48)-net over F₈, using
- net from sequence [i] based on digital (11, 47)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
    - a function field by SÃ©mirat [i]

(34−21, 34, 56)-Net over F₈ — Digital

Digital (13, 34, 56)-net over F₈, using

net from sequence [i] based on digital (13, 55)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 13 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(34−21, 34, 612)-Net in Base 8 — Upper bound on s

There is no (13, 34, 613)-net in base 8, because

1 times m-reduction [i] would yield (13, 33, 613)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 641937 984375 360997 829610 160952 > 8³³ [i]