MinT - Best Known (34, 59, s)-Nets in Base 8

Best Known (34, 59, s)-Nets in Base 8

Digital (34, 59, 208)-net over F₈, using

3 times m-reduction [i] based on digital (34, 62, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 31, 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 (34, 59, 258)-net over F₈, using

1 times m-reduction [i] based on digital (34, 60, 258)-net over F₈, using
- trace code for nets [i] based on digital (4, 30, 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 (34, 59, 17500)-net in base 8, because

1 times m-reduction [i] would yield (34, 58, 17500)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 23957 627126 967232 722106 999310 118655 788800 438825 967876 > 8⁵⁸ [i]