MinT - Best Known (18, 18+37, s)-Nets in Base 32

Best Known (18, 18+37, s)-Nets in Base 32

(18, 18+37, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 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]

(18, 18+37, 161)-Net over F₃₂ — Digital

Digital (18, 55, 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+37, 177)-Net in Base 32 — Constructive

(18, 55, 177)-net in base 32, using

11 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+37, 7974)-Net in Base 32 — Upper bound on s

There is no (18, 55, 7975)-net in base 32, because

1 times m-reduction [i] would yield (18, 54, 7975)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1897 648030 156082 780763 358083 363718 308096 733953 186847 626358 829188 917030 918846 812306 > 32⁵⁴ [i]