MinT - Best Known (20, 20+71, s)-Nets in Base 32

Best Known (20, 20+71, s)-Nets in Base 32

(20, 20+71, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 91, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 91, 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]

(20, 20+71, 177)-Net over F₃₂ — Digital

Digital (20, 91, 177)-net over F₃₂, using

net from sequence [i] based on digital (20, 176)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 20 and N(F) ≥ 177, using
  - a curve from the manYPoints database [i]

(20, 20+71, 3310)-Net in Base 32 — Upper bound on s

There is no (20, 91, 3311)-net in base 32, because

1 times m-reduction [i] would yield (20, 90, 3311)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2916 766043 797148 334882 312662 024112 897498 861324 362701 842296 519333 442630 604166 305288 158330 811572 773147 930801 581956 968325 821112 573864 207212 > 32⁹⁰ [i]