MinT - Best Known (17−11, 17, s)-Nets in Base 32

Best Known (17−11, 17, s)-Nets in Base 32

(17−11, 17, 77)-Net over F₃₂ — Constructive and digital

Digital (6, 17, 77)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 5, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
      - the rational function field F₃₂(x) [i]
    - Niederreiter sequence [i]
2. digital (1, 12, 44)-net over F₃₂, using
  - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]

(17−11, 17, 86)-Net over F₃₂ — Digital

Digital (6, 17, 86)-net over F₃₂, using

net from sequence [i] based on digital (6, 85)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 6 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(17−11, 17, 129)-Net in Base 32 — Constructive

(6, 17, 129)-net in base 32, using

4 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
- base change [i] based on digital (0, 15, 129)-net over F₁₂₈, using
  - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
      - the rational function field F₁₂₈(x) [i]
    - Niederreiter sequence [i]

(17−11, 17, 5505)-Net in Base 32 — Upper bound on s

There is no (6, 17, 5506)-net in base 32, because

1 times m-reduction [i] would yield (6, 16, 5506)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 209651 788168 778367 434208 > 32¹⁶ [i]