MinT - Best Known (67, 67+53, s)-Nets in Base 8

Best Known (67, 67+53, s)-Nets in Base 8

(67, 67+53, 354)-Net over F₈ — Constructive and digital

Digital (67, 120, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 60, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(67, 67+53, 20475)-Net in Base 8 — Upper bound on s

There is no (67, 120, 20476)-net in base 8, because

1 times m-reduction [i] would yield (67, 119, 20476)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 293926 629974 860693 010527 412789 358667 552522 447875 037719 083452 508577 403739 304465 628036 263665 220786 126828 207533 > 8¹¹⁹ [i]