MinT - Best Known (32, 32+60, s)-Nets in Base 32

Best Known (32, 32+60, s)-Nets in Base 32

(32, 32+60, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 92, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 92, 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]

(32, 32+60, 216)-Net in Base 32 — Constructive

(32, 92, 216)-net in base 32, using

32¹ times duplication [i] based on (31, 91, 216)-net in base 32, using
- base change [i] based on digital (5, 65, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(32, 32+60, 273)-Net over F₃₂ — Digital

Digital (32, 92, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 92, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(32, 32+60, 16025)-Net in Base 32 — Upper bound on s

There is no (32, 92, 16026)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 982024 308911 287010 079790 738457 459279 983754 743410 458823 037281 502577 338954 293327 899710 338375 719291 420052 649058 003797 638910 608569 472585 115456 > 32⁹² [i]