MinT - Best Known (59, 59+45, s)-Nets in Base 8

Best Known (59, 59+45, s)-Nets in Base 8

(59, 59+45, 354)-Net over F₈ — Constructive and digital

Digital (59, 104, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 52, 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]

(59, 59+45, 21856)-Net in Base 8 — Upper bound on s

There is no (59, 104, 21857)-net in base 8, because

1 times m-reduction [i] would yield (59, 103, 21857)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1043 141453 974891 543626 634667 799934 325822 468598 152327 038677 586024 170286 757154 121030 749019 329552 > 8¹⁰³ [i]