MinT - Best Known (25−13, 25, s)-Nets in Base 16

Best Known (25−13, 25, s)-Nets in Base 16

(25−13, 25, 257)-Net over F₁₆ — Constructive and digital

Digital (12, 25, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(12,256) in PG(24,16)) for nets [i] based on digital (0, 13, 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]

(25−13, 25, 13077)-Net in Base 16 — Upper bound on s

There is no (12, 25, 13078)-net in base 16, because

1 times m-reduction [i] would yield (12, 24, 13078)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 79257 573679 888452 937697 087896 > 16²⁴ [i]