MinT - Best Known (44, 44+43, s)-Nets in Base 16

Best Known (44, 44+43, s)-Nets in Base 16

(44, 44+43, 514)-Net over F₁₆ — Constructive and digital

Digital (44, 87, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (44, 88, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 44, 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]

(44, 44+43, 49369)-Net in Base 16 — Upper bound on s

There is no (44, 87, 49370)-net in base 16, because

1 times m-reduction [i] would yield (44, 86, 49370)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 35 842951 900109 693341 847596 158510 604151 395339 305661 252509 715463 495212 868949 060241 319506 550016 028630 520926 > 16⁸⁶ [i]