MinT - Best Known (7, 7+45, s)-Nets in Base 32

Best Known (7, 7+45, s)-Nets in Base 32

(7, 7+45, 98)-Net over F₃₂ — Constructive and digital

Digital (7, 52, 98)-net over F₃₂, using

net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
  - a function field by SÃ©mirat [i]

(7, 7+45, 889)-Net in Base 32 — Upper bound on s

There is no (7, 52, 890)-net in base 32, because

1 times m-reduction [i] would yield (7, 51, 890)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 58214 711070 188190 569873 774237 432930 475555 019614 380059 166067 210448 776061 791684 > 32⁵¹ [i]