MinT - Best Known (11, 11+18, s)-Nets in Base 32

Best Known (11, 11+18, s)-Nets in Base 32

(11, 11+18, 120)-Net over F₃₂ — Constructive and digital

Digital (11, 29, 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, 11+18, 150)-Net in Base 32 — Constructive

(11, 29, 150)-net in base 32, using

6 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, 11+18, 172)-Net in Base 32

(11, 29, 172)-net in base 32, using

1 times m-reduction [i] based on (11, 30, 172)-net in base 32, using
- base change [i] based on (6, 25, 172)-net in base 64, using
  - 3 times m-reduction [i] based on (6, 28, 172)-net in base 64, using
    - base change [i] based on digital (2, 24, 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]

(11, 11+18, 9465)-Net in Base 32 — Upper bound on s

There is no (11, 29, 9466)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 44 643851 118001 393520 540843 110842 801092 001645 > 32²⁹ [i]