MinT - Best Known (15−8, 15, s)-Nets in Base 16

Best Known (15−8, 15, s)-Nets in Base 16

(15−8, 15, 257)-Net over F₁₆ — Constructive and digital

Digital (7, 15, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(7,256) in PG(14,16)) for nets [i] based on digital (0, 8, 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]

(15−8, 15, 4833)-Net in Base 16 — Upper bound on s

There is no (7, 15, 4834)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 153493 271623 021416 > 16¹⁵ [i]