MinT - Best Known (57−39, 57, s)-Nets in Base 32

Best Known (57−39, 57, s)-Nets in Base 32

(57−39, 57, 120)-Net over F₃₂ — Constructive and digital

Digital (18, 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]

(57−39, 57, 161)-Net over F₃₂ — Digital

Digital (18, 57, 161)-net over F₃₂, using

net from sequence [i] based on digital (18, 160)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 18 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(57−39, 57, 177)-Net in Base 32 — Constructive

(18, 57, 177)-net in base 32, using

9 times m-reduction [i] based on (18, 66, 177)-net in base 32, using
- base change [i] based on digital (7, 55, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(57−39, 57, 6974)-Net in Base 32 — Upper bound on s

There is no (18, 57, 6975)-net in base 32, because

1 times m-reduction [i] would yield (18, 56, 6975)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 947504 898808 660549 704990 399158 187842 938908 004800 275412 131366 011561 582101 977437 679556 > 32⁵⁶ [i]