MinT - Best Known (109−89, 109, s)-Nets in Base 32

Best Known (109−89, 109, s)-Nets in Base 32

(109−89, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 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]

(109−89, 109, 177)-Net over F₃₂ — Digital

Digital (20, 109, 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]

(109−89, 109, 2731)-Net in Base 32 — Upper bound on s

There is no (20, 109, 2732)-net in base 32, because

1 times m-reduction [i] would yield (20, 108, 2732)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 629313 311458 505661 161085 634468 371756 291235 387882 119253 112075 994028 601257 810115 182659 156928 346053 269181 566919 961145 387238 280971 253200 546762 976061 341438 804182 289120 > 32¹⁰⁸ [i]