MinT - Best Known (19, 19+73, s)-Nets in Base 32

Best Known (19, 19+73, s)-Nets in Base 32

(19, 19+73, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 92, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 92, 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+73, 172)-Net over F₃₂ — Digital

Digital (19, 92, 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+73, 2919)-Net in Base 32 — Upper bound on s

There is no (19, 92, 2920)-net in base 32, because

1 times m-reduction [i] would yield (19, 91, 2920)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93698 680183 713097 911365 091752 917204 369418 466471 934356 177669 584588 434793 588880 583630 606673 888007 281047 762024 910925 888268 305881 997635 574757 > 32⁹¹ [i]