MinT - Best Known (5, 5+9, s)-Nets in Base 32

Best Known (5, 5+9, s)-Nets in Base 32

(5, 5+9, 77)-Net over F₃₂ — Constructive and digital

Digital (5, 14, 77)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 4, 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, 10, 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]

(5, 5+9, 83)-Net over F₃₂ — Digital

Digital (5, 14, 83)-net over F₃₂, using

net from sequence [i] based on digital (5, 82)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 83, using
  - a curve from the manYPoints database [i]

(5, 5+9, 150)-Net in Base 32 — Constructive

(5, 14, 150)-net in base 32, using

base change [i] based on digital (1, 10, 150)-net over F₁₂₈, using
- net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(5, 5+9, 5562)-Net in Base 32 — Upper bound on s

There is no (5, 14, 5563)-net in base 32, because

1 times m-reduction [i] would yield (5, 13, 5563)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 36 896090 968760 844334 > 32¹³ [i]