MinT - Best Known (14, 29, s)-Nets in Base 16

Best Known (14, 29, s)-Nets in Base 16

(14, 29, 257)-Net over F₁₆ — Constructive and digital

Digital (14, 29, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(14,256) in PG(28,16)) for nets [i] based on digital (0, 15, 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]

(14, 29, 14764)-Net in Base 16 — Upper bound on s

There is no (14, 29, 14765)-net in base 16, because

1 times m-reduction [i] would yield (14, 28, 14765)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 5194 647447 459303 988969 736574 973576 > 16²⁸ [i]