MinT - Best Known (36, 36+22, s)-Nets in Base 16

Best Known (36, 36+22, s)-Nets in Base 16

(36, 36+22, 552)-Net over F₁₆ — Constructive and digital

Digital (36, 58, 552)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (3, 14, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]
2. digital (22, 44, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 22, 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, 36+22, 1235)-Net over F₁₆ — Digital

Digital (36, 58, 1235)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 36+22, 730997)-Net in Base 16 — Upper bound on s

There is no (36, 58, 730998)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6901 820753 661939 854230 479186 287342 693489 820690 094901 883276 561950 970796 > 16⁵⁸ [i]