MinT - Best Known (22, 56, s)-Nets in Base 16

Best Known (22, 56, s)-Nets in Base 16

(22, 56, 71)-Net over F₁₆ — Constructive and digital

Digital (22, 56, 71)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 19, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. digital (3, 37, 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]

(22, 56, 104)-Net in Base 16 — Constructive

(22, 56, 104)-net in base 16, using

9 times m-reduction [i] based on (22, 65, 104)-net in base 16, using
- base change [i] based on digital (9, 52, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(22, 56, 129)-Net over F₁₆ — Digital

Digital (22, 56, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 56, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(22, 56, 4420)-Net in Base 16 — Upper bound on s

There is no (22, 56, 4421)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 27 012221 105580 166845 254656 781049 658400 264584 184911 686486 750954 013456 > 16⁵⁶ [i]