MinT - Best Known (25, 51, s)-Nets in Base 16

Best Known (25, 51, s)-Nets in Base 16

(25, 51, 257)-Net over F₁₆ — Constructive and digital

Digital (25, 51, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(25,256) in PG(50,16)) for nets [i] based on digital (0, 26, 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, 51, 19999)-Net in Base 16 — Upper bound on s

There is no (25, 51, 20000)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 25 717804 249156 744059 466533 950324 208269 291785 159165 817681 587501 > 16⁵¹ [i]