MinT - Best Known (31, 31+55, s)-Nets in Base 32

Best Known (31, 31+55, s)-Nets in Base 32

(31, 31+55, 120)-Net over F₃₂ — Constructive and digital

Digital (31, 86, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 86, 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]

(31, 31+55, 216)-Net in Base 32 — Constructive

(31, 86, 216)-net in base 32, using

5 times m-reduction [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]

(31, 31+55, 273)-Net over F₃₂ — Digital

Digital (31, 86, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 86, 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]

(31, 31+55, 19282)-Net in Base 32 — Upper bound on s

There is no (31, 86, 19283)-net in base 32, because

1 times m-reduction [i] would yield (31, 85, 19283)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 86 681761 203861 286589 169927 924393 202291 462609 931726 601342 959688 602423 013929 725602 689265 698742 631811 968419 670246 028910 522061 486784 > 32⁸⁵ [i]