MinT - Best Known (46−27, 46, s)-Nets in Base 8

Best Known (46−27, 46, s)-Nets in Base 8

(46−27, 46, 65)-Net over F₈ — Constructive and digital

Digital (19, 46, 65)-net over F₈, using

t-expansion [i] based on digital (14, 46, 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]

(46−27, 46, 1074)-Net in Base 8 — Upper bound on s

There is no (19, 46, 1075)-net in base 8, because

1 times m-reduction [i] would yield (19, 45, 1075)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 43784 923943 762946 379902 408789 785269 075416 > 8⁴⁵ [i]