MinT - Best Known (48, 48+47, s)-Nets in Base 16

Best Known (48, 48+47, s)-Nets in Base 16

(48, 48+47, 514)-Net over F₁₆ — Constructive and digital

Digital (48, 95, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (48, 96, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 48, 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]

(48, 48+47, 52413)-Net in Base 16 — Upper bound on s

There is no (48, 95, 52414)-net in base 16, because

1 times m-reduction [i] would yield (48, 94, 52414)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 153914 888959 037116 055886 410443 761369 239879 178954 791527 918966 206731 640598 847628 400503 037498 251251 414710 500122 564956 > 16⁹⁴ [i]