MinT - Best Known (66, 66+49, s)-Nets in Base 16

Best Known (66, 66+49, s)-Nets in Base 16

Digital (66, 115, 530)-net over F₁₆, using

1 times m-reduction [i] based on digital (66, 116, 530)-net over F₁₆, using
- trace code for nets [i] based on digital (8, 58, 265)-net over F₂₅₆, using
  - net from sequence [i] based on digital (8, 264)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

Digital (66, 115, 1026)-net over F₁₆, using

1 times m-reduction [i] based on digital (66, 116, 1026)-net over F₁₆, using
- trace code for nets [i] based on digital (8, 58, 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 (66, 115, 342630)-net in base 16, because

1 times m-reduction [i] would yield (66, 114, 342630)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 186076 838145 232762 909024 649880 870736 421309 660944 119820 714497 269501 229629 357235 330466 304522 319375 200950 780178 271165 586539 915448 603040 247676 > 16¹¹⁴ [i]