MinT - Best Known (50−37, 50, s)-Nets in Base 8

Best Known (50−37, 50, s)-Nets in Base 8

(50−37, 50, 48)-Net over F₈ — Constructive and digital

Digital (13, 50, 48)-net over F₈, using

t-expansion [i] based on digital (11, 50, 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]

(50−37, 50, 56)-Net over F₈ — Digital

Digital (13, 50, 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]

(50−37, 50, 299)-Net in Base 8 — Upper bound on s

There is no (13, 50, 300)-net in base 8, because

1 times m-reduction [i] would yield (13, 49, 300)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 187 863353 574628 137211 770734 643788 179834 315006 > 8⁴⁹ [i]