MinT - Best Known (20, 20+37, s)-Nets in Base 32

Best Known (20, 20+37, s)-Nets in Base 32

(20, 20+37, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 57, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 57, 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]

(20, 20+37, 177)-Net over F₃₂ — Digital

Digital (20, 57, 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]

(20, 20+37, 192)-Net in Base 32 — Constructive

(20, 57, 192)-net in base 32, using

32¹ times duplication [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]

(20, 20+37, 225)-Net in Base 32

(20, 57, 225)-net in base 32, using

3 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]

(20, 20+37, 11725)-Net in Base 32 — Upper bound on s

There is no (20, 57, 11726)-net in base 32, because

1 times m-reduction [i] would yield (20, 56, 11726)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 944992 040253 590862 970038 557640 161148 846619 182746 299087 122030 377850 844150 161218 663784 > 32⁵⁶ [i]