MinT - Best Known (32, 32+23, s)-Nets in Base 8

Best Known (32, 32+23, s)-Nets in Base 8

Digital (32, 55, 208)-net over F₈, using

3 times m-reduction [i] based on digital (32, 58, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 29, 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]

(32, 55, 258)-net in base 8, using

Digital (32, 55, 258)-net over F₈, using

1 times m-reduction [i] based on digital (32, 56, 258)-net over F₈, using
- trace code for nets [i] based on digital (4, 28, 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 (32, 55, 19016)-net in base 8, because

1 times m-reduction [i] would yield (32, 54, 19016)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 846339 027415 145373 943769 468967 730128 599562 977576 > 8⁵⁴ [i]