MinT - Best Known (21, 21+85, s)-Nets in Base 32

Best Known (21, 21+85, s)-Nets in Base 32

(21, 21+85, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 106, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 106, 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]

(21, 21+85, 185)-Net over F₃₂ — Digital

Digital (21, 106, 185)-net over F₃₂, using

net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
  - a curve from the manYPoints database [i]

(21, 21+85, 3063)-Net in Base 32 — Upper bound on s

There is no (21, 106, 3064)-net in base 32, because

1 times m-reduction [i] would yield (21, 105, 3064)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 110 430295 985558 556189 410655 865519 301367 624604 647391 015703 241865 575907 879162 225198 524092 673719 858346 743230 086824 027915 964381 270760 979608 509048 342294 456888 219258 > 32¹⁰⁵ [i]