MinT - Best Known (99−49, 99, s)-Nets in Base 16

Best Known (99−49, 99, s)-Nets in Base 16

(99−49, 99, 514)-Net over F₁₆ — Constructive and digital

Digital (50, 99, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (50, 100, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 50, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(99−49, 99, 53949)-Net in Base 16 — Upper bound on s

There is no (50, 99, 53950)-net in base 16, because

1 times m-reduction [i] would yield (50, 98, 53950)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10088 108924 872458 435833 218291 280188 009662 590803 205397 306272 865866 259338 868203 482307 415479 473510 984950 343961 697472 407001 > 16⁹⁸ [i]