MinT - Best Known (15−7, 15, s)-Nets in Base 16

Best Known (15−7, 15, s)-Nets in Base 16

(15−7, 15, 514)-Net over F₁₆ — Constructive and digital

Digital (8, 15, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (8, 16, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 8, 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]

(15−7, 15, 50409)-Net in Base 16 — Upper bound on s

There is no (8, 15, 50410)-net in base 16, because

1 times m-reduction [i] would yield (8, 14, 50410)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 72061 555646 958076 > 16¹⁴ [i]