MinT - Best Known (53−27, 53, s)-Nets in Base 16

Best Known (53−27, 53, s)-Nets in Base 16

(53−27, 53, 257)-Net over F₁₆ — Constructive and digital

Digital (26, 53, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(26,256) in PG(52,16)) for nets [i] based on digital (0, 27, 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]

(53−27, 53, 24755)-Net in Base 16 — Upper bound on s

There is no (26, 53, 24756)-net in base 16, because

1 times m-reduction [i] would yield (26, 52, 24756)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 411 450776 231523 259583 460663 838198 370771 718834 906316 105121 465596 > 16⁵² [i]