MinT - Best Known (19, 19+37, s)-Nets in Base 32

Best Known (19, 19+37, s)-Nets in Base 32

(19, 19+37, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 56, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 56, 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]

(19, 19+37, 172)-Net over F₃₂ — Digital

Digital (19, 56, 172)-net over F₃₂, using

net from sequence [i] based on digital (19, 171)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 19 and N(F) ≥ 172, using
  - a curve from the manYPoints database [i]

(19, 19+37, 192)-Net in Base 32 — Constructive

(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]

(19, 19+37, 209)-Net in Base 32

(19, 56, 209)-net in base 32, using

4 times m-reduction [i] based on (19, 60, 209)-net in base 32, using
- base change [i] based on digital (9, 50, 209)-net over F₆₄, using
  - net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
      - a curve from the manYPoints database [i]

(19, 19+37, 9670)-Net in Base 32 — Upper bound on s

There is no (19, 56, 9671)-net in base 32, because

1 times m-reduction [i] would yield (19, 55, 9671)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 60812 026949 554595 420190 425755 594356 802520 733994 463088 302081 331630 829798 135108 551148 > 32⁵⁵ [i]