MinT - Best Known (108−72, 108, s)-Nets in Base 32

Best Known (108−72, 108, s)-Nets in Base 32

(108−72, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (36, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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]

(108−72, 108, 216)-Net in Base 32 — Constructive

(36, 108, 216)-net in base 32, using

base change [i] based on (18, 90, 216)-net in base 64, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
  - base change [i] based on digital (5, 78, 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]

(108−72, 108, 273)-Net over F₃₂ — Digital

Digital (36, 108, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 108, 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]

(108−72, 108, 281)-Net in Base 32

(36, 108, 281)-net in base 32, using

base change [i] based on digital (18, 90, 281)-net over F₆₄, using
- net from sequence [i] based on digital (18, 280)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 18 and N(F) ≥ 281, using
    - a curve from the manYPoints database [i]

(108−72, 108, 15076)-Net in Base 32 — Upper bound on s

There is no (36, 108, 15077)-net in base 32, because

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]