MinT - Best Known (55, 55+41, s)-Nets in Base 8

Best Known (55, 55+41, s)-Nets in Base 8

(55, 55+41, 354)-Net over F₈ — Constructive and digital

Digital (55, 96, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 48, 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]

(55, 55+41, 23102)-Net in Base 8 — Upper bound on s

There is no (55, 96, 23103)-net in base 8, because

1 times m-reduction [i] would yield (55, 95, 23103)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 62 208190 169741 767787 349683 983710 955734 816129 372142 710075 219023 754967 666361 879906 218121 > 8⁹⁵ [i]