MinT - Best Known (19, 108, s)-Nets in Base 32

Best Known (19, 108, s)-Nets in Base 32

(19, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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, 108, 172)-Net over F₃₂ — Digital

Digital (19, 108, 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, 108, 2522)-Net in Base 32 — Upper bound on s

There is no (19, 108, 2523)-net in base 32, because

1 times m-reduction [i] would yield (19, 107, 2523)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112758 536362 382822 129655 363344 006497 214757 070961 009122 606279 149251 198408 769199 371312 009888 124402 672060 161952 782733 370715 596327 742922 408672 458779 277520 794439 130568 > 32¹⁰⁷ [i]