MinT - Best Known (10, 51, s)-Nets in Base 32

Best Known (10, 51, s)-Nets in Base 32

(10, 51, 104)-Net over F₃₂ — Constructive and digital

Digital (10, 51, 104)-net over F₃₂, using

t-expansion [i] based on digital (9, 51, 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]

(10, 51, 113)-Net over F₃₂ — Digital

Digital (10, 51, 113)-net over F₃₂, using

net from sequence [i] based on digital (10, 112)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 10 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(10, 51, 1541)-Net in Base 32 — Upper bound on s

There is no (10, 51, 1542)-net in base 32, because

1 times m-reduction [i] would yield (10, 50, 1542)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1818 332534 547605 627120 427234 378634 968687 847416 458200 595401 222491 147304 584352 > 32⁵⁰ [i]