MinT - Best Known (107−45, 107, s)-Nets in Base 16

Best Known (107−45, 107, s)-Nets in Base 16

Digital (62, 107, 530)-net over F₁₆, using

1 times m-reduction [i] based on digital (62, 108, 530)-net over F₁₆, using
- trace code for nets [i] based on digital (8, 54, 265)-net over F₂₅₆, using
  - net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (62, 107, 1026)-net over F₁₆, using

1 times m-reduction [i] based on digital (62, 108, 1026)-net over F₁₆, using
- trace code for nets [i] based on digital (8, 54, 513)-net over F₂₅₆, using
  - net from sequence [i] based on digital (8, 512)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 8 and N(F) ≥ 513, using
      - K_1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F₂₅₆ [i]

There is no (62, 107, 382312)-net in base 16, because

1 times m-reduction [i] would yield (62, 106, 382312)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 43 324605 743601 189725 214201 905748 568688 985080 211491 736464 949268 347832 730771 703379 834011 112998 760542 270113 512372 231038 446046 828886 > 16¹⁰⁶ [i]