MinT - Best Known (90−57, 90, s)-Nets in Base 32

Best Known (90−57, 90, s)-Nets in Base 32

(90−57, 90, 120)-Net over F₃₂ — Constructive and digital

Digital (33, 90, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 90, 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]

(90−57, 90, 216)-Net in Base 32 — Constructive

(33, 90, 216)-net in base 32, using

8 times m-reduction [i] based on (33, 98, 216)-net in base 32, using
- base change [i] based on digital (5, 70, 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]

(90−57, 90, 273)-Net over F₃₂ — Digital

Digital (33, 90, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 90, 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]

(90−57, 90, 281)-Net in Base 32

(33, 90, 281)-net in base 32, using

base change [i] based on digital (18, 75, 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]

(90−57, 90, 22160)-Net in Base 32 — Upper bound on s

There is no (33, 90, 22161)-net in base 32, because

1 times m-reduction [i] would yield (33, 89, 22161)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 90 863236 636751 106212 748293 455851 924855 456979 963120 544046 860085 635012 217172 657871 268065 462397 887513 447405 352370 612127 651737 342530 847584 > 32⁸⁹ [i]