MinT - Best Known (15, 15+45, s)-Nets in Base 8

Best Known (15, 15+45, s)-Nets in Base 8

(15, 15+45, 65)-Net over F₈ — Constructive and digital

Digital (15, 60, 65)-net over F₈, using

t-expansion [i] based on digital (14, 60, 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]

(15, 15+45, 328)-Net in Base 8 — Upper bound on s

There is no (15, 60, 329)-net in base 8, because

1 times m-reduction [i] would yield (15, 59, 329)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 201034 768620 730922 498631 539829 077118 405107 130571 767312 > 8⁵⁹ [i]