MinT - Best Known (18, 109, s)-Nets in Base 32

Best Known (18, 109, s)-Nets in Base 32

(18, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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]

(18, 109, 161)-Net over F₃₂ — Digital

Digital (18, 109, 161)-net over F₃₂, using

net from sequence [i] based on digital (18, 160)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 18 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(18, 109, 2305)-Net in Base 32 — Upper bound on s

There is no (18, 109, 2306)-net in base 32, because

1 times m-reduction [i] would yield (18, 108, 2306)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 626259 497208 904139 406238 274376 904432 273817 219938 863425 002498 467412 064287 960801 076551 049724 269505 779434 013659 141614 801885 515070 265890 503030 454389 071956 314055 724992 > 32¹⁰⁸ [i]