MinT - Best Known (46−35, 46, s)-Nets in Base 32

Best Known (46−35, 46, s)-Nets in Base 32

(46−35, 46, 120)-Net over F₃₂ — Constructive and digital

Digital (11, 46, 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]

(46−35, 46, 2224)-Net in Base 32 — Upper bound on s

There is no (11, 46, 2225)-net in base 32, because

1 times m-reduction [i] would yield (11, 45, 2225)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 54 322161 932687 694054 803505 847339 309252 146376 502277 073688 528566 985856 > 32⁴⁵ [i]