MinT - Best Known (109−73, 109, s)-Nets in Base 32

Best Known (109−73, 109, s)-Nets in Base 32

(109−73, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (36, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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]

(109−73, 109, 192)-Net in Base 32 — Constructive

(36, 109, 192)-net in base 32, using

32¹ times duplication [i] based on (35, 108, 192)-net in base 32, using
- t-expansion [i] based on (34, 108, 192)-net in base 32, using
  - base change [i] based on (16, 90, 192)-net in base 64, using
    - 1 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
      - base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
        net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(109−73, 109, 273)-Net over F₃₂ — Digital

Digital (36, 109, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 109, 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]

(109−73, 109, 15076)-Net in Base 32 — Upper bound on s

There is no (36, 109, 15077)-net in base 32, because

1 times m-reduction [i] would yield (36, 108, 15077)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 607097 057004 804955 150867 967305 715260 974186 383520 585478 045106 603489 589067 520189 635621 178204 299612 574769 805185 701857 868051 861543 937895 879064 619323 055233 628480 087195 > 32¹⁰⁸ [i]