MinT - Best Known (35−18, 35, s)-Nets in Base 16

Best Known (35−18, 35, s)-Nets in Base 16

(35−18, 35, 257)-Net over F₁₆ — Constructive and digital

Digital (17, 35, 257)-net over F₁₆, using

base reduction for projective spaces (embedding PG(17,256) in PG(34,16)) for nets [i] based on digital (0, 18, 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]

(35−18, 35, 13310)-Net in Base 16 — Upper bound on s

There is no (17, 35, 13311)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 394135 008979 647738 483450 449374 723793 342586 > 16³⁵ [i]