MinT - Best Known (75−33, 75, s)-Nets in Base 8

Best Known (75−33, 75, s)-Nets in Base 8

Digital (42, 75, 208)-net over F₈, using

3 times m-reduction [i] based on digital (42, 78, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 39, 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]

Digital (42, 75, 258)-net over F₈, using

1 times m-reduction [i] based on digital (42, 76, 258)-net over F₈, using
- trace code for nets [i] based on digital (4, 38, 129)-net over F₆₄, using
  - net from sequence [i] based on digital (4, 128)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 4 and N(F) ≥ 129, using
      - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₆₄ [i]

There is no (42, 75, 14587)-net in base 8, because

1 times m-reduction [i] would yield (42, 74, 14587)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 746270 968647 377629 348625 370360 773282 074484 998388 855282 053167 658765 > 8⁷⁴ [i]