MinT - Best Known (31−25, 31, s)-Nets in Base 32

Best Known (31−25, 31, s)-Nets in Base 32

(31−25, 31, 76)-Net over F₃₂ — Constructive and digital

Digital (6, 31, 76)-net over F₃₂, using

t-expansion [i] based on digital (5, 31, 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]

(31−25, 31, 86)-Net over F₃₂ — Digital

Digital (6, 31, 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]

(31−25, 31, 982)-Net in Base 32 — Upper bound on s

There is no (6, 31, 983)-net in base 32, because

1 times m-reduction [i] would yield (6, 30, 983)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1437 872768 609366 768380 579058 033012 539178 977374 > 32³⁰ [i]