MinT - Best Known (49, 49+43, s)-Nets in Base 8

Best Known (49, 49+43, s)-Nets in Base 8

(49, 49+43, 208)-Net over F₈ — Constructive and digital

Digital (49, 92, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 46, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(49, 49+43, 226)-Net over F₈ — Digital

Digital (49, 92, 226)-net over F₈, using

trace code for nets [i] based on digital (3, 46, 113)-net over F₆₄, using
- net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
    - a curve from the manYPoints database [i]

(49, 49+43, 10144)-Net in Base 8 — Upper bound on s

There is no (49, 92, 10145)-net in base 8, because

1 times m-reduction [i] would yield (49, 91, 10145)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 15194 368631 051402 359973 674038 172855 881416 993244 470072 710715 882940 400821 116089 960928 > 8⁹¹ [i]