MinT - Best Known (48−39, 48, s)-Nets in Base 32

Best Known (48−39, 48, s)-Nets in Base 32

(48−39, 48, 104)-Net over F₃₂ — Constructive and digital

Digital (9, 48, 104)-net over F₃₂, using

net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
  - a function field by SÃ©mirat [i]

(48−39, 48, 108)-Net over F₃₂ — Digital

Digital (9, 48, 108)-net over F₃₂, using

net from sequence [i] based on digital (9, 107)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 108, using
  - a curve from the manYPoints database [i]

(48−39, 48, 1342)-Net in Base 32 — Upper bound on s

There is no (9, 48, 1343)-net in base 32, because

1 times m-reduction [i] would yield (9, 47, 1343)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 55332 632863 431809 160831 055681 780667 588569 144033 039854 448302 715926 237252 > 32⁴⁷ [i]