MinT - Best Known (51−45, 51, s)-Nets in Base 32

Best Known (51−45, 51, s)-Nets in Base 32

(51−45, 51, 76)-Net over F₃₂ — Constructive and digital

Digital (6, 51, 76)-net over F₃₂, using

t-expansion [i] based on digital (5, 51, 76)-net over F₃₂, using
- net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(51−45, 51, 86)-Net over F₃₂ — Digital

Digital (6, 51, 86)-net over F₃₂, using

net from sequence [i] based on digital (6, 85)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 6 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(51−45, 51, 758)-Net in Base 32 — Upper bound on s

There is no (6, 51, 759)-net in base 32, because

1 times m-reduction [i] would yield (6, 50, 759)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1837 135158 128384 281239 635639 154252 494160 370192 512741 871331 460775 390936 339547 > 32⁵⁰ [i]