MinT - Best Known (89−57, 89, s)-Nets in Base 32

Best Known (89−57, 89, s)-Nets in Base 32

(89−57, 89, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 89, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 89, 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]

(89−57, 89, 216)-Net in Base 32 — Constructive

(32, 89, 216)-net in base 32, using

t-expansion [i] based on (31, 89, 216)-net in base 32, using
- 2 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]

(89−57, 89, 273)-Net over F₃₂ — Digital

Digital (32, 89, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 89, 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]

(89−57, 89, 19579)-Net in Base 32 — Upper bound on s

There is no (32, 89, 19580)-net in base 32, because

1 times m-reduction [i] would yield (32, 88, 19580)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 842381 192876 322808 060703 225905 473143 728249 297527 144507 748307 525156 873454 345136 972973 587120 116862 102507 155629 668076 238729 038033 540440 > 32⁸⁸ [i]