MinT - Best Known (16−11, 16, s)-Nets in Base 256

Best Known (16−11, 16, s)-Nets in Base 256

(16−11, 16, 514)-Net over F₂₅₆ — Constructive and digital

Digital (5, 16, 514)-net over F₂₅₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 5, 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, 11, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(16−11, 16, 171400)-Net in Base 256 — Upper bound on s

There is no (5, 16, 171401)-net in base 256, because

1 times m-reduction [i] would yield (5, 15, 171401)-net in base 256, but
- the generalized Rao bound for nets shows that 256^mÂ â‰¥ 1 329266 314217 885560 482850 552778 312776 > 256¹⁵ [i]