MinT - Best Known (55−35, 55, s)-Nets in Base 32

Best Known (55−35, 55, s)-Nets in Base 32

(55−35, 55, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 55, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 55, 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]

(55−35, 55, 177)-Net over F₃₂ — Digital

Digital (20, 55, 177)-net over F₃₂, using

net from sequence [i] based on digital (20, 176)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 20 and N(F) ≥ 177, using
  - a curve from the manYPoints database [i]

(55−35, 55, 192)-Net in Base 32 — Constructive

(20, 55, 192)-net in base 32, using

t-expansion [i] based on (19, 55, 192)-net in base 32, using
- 1 times m-reduction [i] based on (19, 56, 192)-net in base 32, using
  - base change [i] based on digital (3, 40, 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]

(55−35, 55, 225)-Net in Base 32

(20, 55, 225)-net in base 32, using

5 times m-reduction [i] based on (20, 60, 225)-net in base 32, using
- base change [i] based on digital (10, 50, 225)-net over F₆₄, using
  - net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
      - a curve from the manYPoints database [i]

(55−35, 55, 13975)-Net in Base 32 — Upper bound on s

There is no (20, 55, 13976)-net in base 32, because

1 times m-reduction [i] would yield (20, 54, 13976)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1897 156846 042126 886107 116663 566211 402371 104888 590527 897286 353655 162966 356482 536837 > 32⁵⁴ [i]