MinT - Best Known (36−18, 36, s)-Nets in Base 16

Best Known (36−18, 36, s)-Nets in Base 16

(36−18, 36, 514)-Net over F₁₆ — Constructive and digital

Digital (18, 36, 514)-net over F₁₆, using

trace code 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]

(36−18, 36, 18114)-Net in Base 16 — Upper bound on s

There is no (18, 36, 18115)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 22 304663 925332 073328 663158 694733 066959 433776 > 16³⁶ [i]