MinT - Best Known (19, 19+85, s)-Nets in Base 32

Best Known (19, 19+85, s)-Nets in Base 32

(19, 19+85, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 104, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 104, 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+85, 172)-Net over F₃₂ — Digital

Digital (19, 104, 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+85, 2594)-Net in Base 32 — Upper bound on s

There is no (19, 104, 2595)-net in base 32, because

1 times m-reduction [i] would yield (19, 103, 2595)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 108639 023492 449907 195149 723964 788244 825474 203891 275691 146346 105343 876007 602022 297723 610068 928341 489141 033262 681093 368606 972914 311759 903259 505047 999584 826560 > 32¹⁰³ [i]