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

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

(11, 32, 120)-Net over F₃₂ — Constructive and digital

Digital (11, 32, 120)-net over F₃₂, using

net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
  - a function field by SÃ©mirat [i]

(11, 32, 150)-Net in Base 32 — Constructive

(11, 32, 150)-net in base 32, using

3 times m-reduction [i] based on (11, 35, 150)-net in base 32, using
- base change [i] based on digital (1, 25, 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]

(11, 32, 6765)-Net in Base 32 — Upper bound on s

There is no (11, 32, 6766)-net in base 32, because

1 times m-reduction [i] would yield (11, 31, 6766)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 45737 003902 826033 658914 476948 059742 177289 172294 > 32³¹ [i]