MinT - Best Known (47, 47+33, s)-Nets in Base 8

Best Known (47, 47+33, s)-Nets in Base 8

(47, 47+33, 354)-Net over F₈ — Constructive and digital

Digital (47, 80, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 40, 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]

(47, 47+33, 27944)-Net in Base 8 — Upper bound on s

There is no (47, 80, 27945)-net in base 8, because

1 times m-reduction [i] would yield (47, 79, 27945)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 220926 320040 334887 485546 241027 275788 673909 843079 625913 837250 323127 006370 > 8⁷⁹ [i]