MinT - Best Known (12, 57, s)-Nets in Base 32

Best Known (12, 57, s)-Nets in Base 32

(12, 57, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 57, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 57, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(12, 57, 129)-Net over F₃₂ — Digital

Digital (12, 57, 129)-net over F₃₂, using

net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(12, 57, 1969)-Net in Base 32 — Upper bound on s

There is no (12, 57, 1970)-net in base 32, because

1 times m-reduction [i] would yield (12, 56, 1970)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 957008 545892 833724 722553 204567 209618 983084 958306 911042 201422 686371 622702 194116 189072 > 32⁵⁶ [i]