MinT - Best Known (48−37, 48, s)-Nets in Base 8

Best Known (48−37, 48, s)-Nets in Base 8

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

Digital (11, 48, 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]

(48−37, 48, 235)-Net in Base 8 — Upper bound on s

There is no (11, 48, 236)-net in base 8, because

1 times m-reduction [i] would yield (11, 47, 236)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 960655 764194 350382 468762 740640 588791 617362 > 8⁴⁷ [i]