MinT - Best Known (127−63, 127, s)-Nets in Base 16

Best Known (127−63, 127, s)-Nets in Base 16

(127−63, 127, 514)-Net over F₁₆ — Constructive and digital

Digital (64, 127, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (64, 128, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 64, 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]

(127−63, 127, 64862)-Net in Base 16 — Upper bound on s

There is no (64, 127, 64863)-net in base 16, because

1 times m-reduction [i] would yield (64, 126, 64863)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 52 391030 333002 443441 803143 200753 294217 690396 027670 141458 018762 379074 920985 220857 940056 628977 229129 514562 374538 696160 450944 073042 064058 919030 041379 885296 > 16¹²⁶ [i]