MinT - Best Known (17, 52, s)-Nets in Base 256

Best Known (17, 52, s)-Nets in Base 256

(17, 52, 514)-Net over F₂₅₆ — Constructive and digital

Digital (17, 52, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 17, 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]
2. digital (0, 35, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(17, 52, 472190)-Net in Base 256 — Upper bound on s

There is no (17, 52, 472191)-net in base 256, because

1 times m-reduction [i] would yield (17, 51, 472191)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 661 061196 639057 307988 947834 774933 529587 798696 375812 533292 034829 356548 975536 947127 883951 003165 715710 109262 612830 897461 740386 > 256⁵¹ [i]