MinT - Best Known (54, 54+54, s)-Nets in Base 16

Best Known (54, 54+54, s)-Nets in Base 16

(54, 54+54, 514)-Net over F₁₆ — Constructive and digital

Digital (54, 108, 514)-net over F₁₆, using

trace code for nets [i] based on digital (0, 54, 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]

(54, 54+54, 47715)-Net in Base 16 — Upper bound on s

There is no (54, 108, 47716)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11092 927721 572884 076007 765059 713824 776239 868805 359137 019631 405924 811101 110068 390300 265465 487591 160404 118265 176983 688975 616508 054956 > 16¹⁰⁸ [i]