MinT - Best Known (9, 29, s)-Nets in Base 32

Best Known (9, 29, s)-Nets in Base 32

(9, 29, 104)-Net over F₃₂ — Constructive and digital

Digital (9, 29, 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]

(9, 29, 108)-Net over F₃₂ — Digital

Digital (9, 29, 108)-net over F₃₂, using

net from sequence [i] based on digital (9, 107)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 108, using
  - a curve from the manYPoints database [i]

(9, 29, 129)-Net in Base 32 — Constructive

(9, 29, 129)-net in base 32, using

1 times m-reduction [i] based on (9, 30, 129)-net in base 32, using
- base change [i] based on (4, 25, 129)-net in base 64, using
  - 3 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
    - base change [i] based on digital (0, 24, 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]

(9, 29, 3380)-Net in Base 32 — Upper bound on s

There is no (9, 29, 3381)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 44 719171 206942 200190 241710 594251 828901 165788 > 32²⁹ [i]