MinT - Best Known (18, 48, s)-Nets in Base 32

Best Known (18, 48, s)-Nets in Base 32

(18, 48, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 48, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 48, 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, 48, 161)-Net over F₃₂ — Digital

Digital (18, 48, 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, 48, 257)-Net in Base 32 — Constructive

(18, 48, 257)-net in base 32, using

base change [i] based on digital (0, 30, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(18, 48, 13572)-Net in Base 32 — Upper bound on s

There is no (18, 48, 13573)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 768699 302078 728392 572666 463989 422074 078737 552850 263344 951009 628958 510336 > 32⁴⁸ [i]