MinT - Best Known (18, 18+35, s)-Nets in Base 32

Best Known (18, 18+35, s)-Nets in Base 32

(18, 18+35, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 53, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 53, 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]

(18, 18+35, 161)-Net over F₃₂ — Digital

Digital (18, 53, 161)-net over F₃₂, using

net from sequence [i] based on digital (18, 160)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 18 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(18, 18+35, 177)-Net in Base 32 — Constructive

(18, 53, 177)-net in base 32, using

13 times m-reduction [i] based on (18, 66, 177)-net in base 32, using
- base change [i] based on digital (7, 55, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(18, 18+35, 209)-Net in Base 32

(18, 53, 209)-net in base 32, using

1 times m-reduction [i] based on (18, 54, 209)-net in base 32, using
- base change [i] based on digital (9, 45, 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]

(18, 18+35, 9293)-Net in Base 32 — Upper bound on s

There is no (18, 53, 9294)-net in base 32, because

1 times m-reduction [i] would yield (18, 52, 9294)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 854862 882194 563690 675642 275346 750949 020580 132756 987698 618655 458803 709350 042252 > 32⁵² [i]