MinT - Best Known (14, 14+31, s)-Nets in Base 32

Best Known (14, 14+31, s)-Nets in Base 32

(14, 14+31, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 45, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 45, 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]

(14, 14+31, 129)-Net in Base 32 — Constructive

(14, 45, 129)-net in base 32, using

4 times m-reduction [i] based on (14, 49, 129)-net in base 32, using
- base change [i] based on digital (0, 35, 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]

(14, 14+31, 146)-Net over F₃₂ — Digital

Digital (14, 45, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(14, 14+31, 161)-Net in Base 32

(14, 45, 161)-net in base 32, using

3 times m-reduction [i] based on (14, 48, 161)-net in base 32, using
- base change [i] based on digital (6, 40, 161)-net over F₆₄, using
  - net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(14, 14+31, 5381)-Net in Base 32 — Upper bound on s

There is no (14, 45, 5382)-net in base 32, because

1 times m-reduction [i] would yield (14, 44, 5382)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 687060 153576 701145 052971 951774 898232 923325 161789 081182 867298 165120 > 32⁴⁴ [i]