MinT - Best Known (12, 12+21, s)-Nets in Base 32

Best Known (12, 12+21, s)-Nets in Base 32

(12, 12+21, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 33, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 33, 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]

(12, 12+21, 129)-Net over F₃₂ — Digital

Digital (12, 33, 129)-net over F₃₂, using

net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(12, 12+21, 150)-Net in Base 32 — Constructive

(12, 33, 150)-net in base 32, using

t-expansion [i] based on (11, 33, 150)-net in base 32, using
- 2 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]

(12, 12+21, 172)-Net in Base 32

(12, 33, 172)-net in base 32, using

2 times m-reduction [i] based on (12, 35, 172)-net in base 32, using
- base change [i] based on digital (2, 25, 172)-net over F₁₂₈, using
  - net from sequence [i] based on digital (2, 171)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 2 and N(F) ≥ 172, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(12, 12+21, 9569)-Net in Base 32 — Upper bound on s

There is no (12, 33, 9570)-net in base 32, because

1 times m-reduction [i] would yield (12, 32, 9570)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 462719 302224 002015 788687 990352 901410 856630 955184 > 32³² [i]