MinT - Best Known (86−67, 86, s)-Nets in Base 32

Best Known (86−67, 86, s)-Nets in Base 32

(86−67, 86, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 86, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 86, 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]

(86−67, 86, 172)-Net over F₃₂ — Digital

Digital (19, 86, 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]

(86−67, 86, 3181)-Net in Base 32 — Upper bound on s

There is no (19, 86, 3182)-net in base 32, because

1 times m-reduction [i] would yield (19, 85, 3182)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 87 482491 427578 307147 127450 624078 499779 755543 526389 911601 710393 321880 250035 103418 350169 891963 011002 951294 687049 375257 683296 406465 > 32⁸⁵ [i]