MinT - Best Known (4, 4+36, s)-Nets in Base 32

Best Known (4, 4+36, s)-Nets in Base 32

(4, 4+36, 64)-Net over F₃₂ — Constructive and digital

Digital (4, 40, 64)-net over F₃₂, using

t-expansion [i] based on digital (3, 40, 64)-net over F₃₂, using
- net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
    - a function field by SÃ©mirat [i]

(4, 4+36, 71)-Net over F₃₂ — Digital

Digital (4, 40, 71)-net over F₃₂, using

net from sequence [i] based on digital (4, 70)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 4 and N(F) ≥ 71, using
  - a curve from the manYPoints database [i]

(4, 4+36, 526)-Net in Base 32 — Upper bound on s

There is no (4, 40, 527)-net in base 32, because

4 times m-reduction [i] would yield (4, 36, 527)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 565609 455691 255002 140952 023254 084028 302343 434446 899744 > 32³⁶ [i]