MinT - Best Known (57−35, 57, s)-Nets in Base 32

Best Known (57−35, 57, s)-Nets in Base 32

(57−35, 57, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 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]

(57−35, 57, 185)-Net over F₃₂ — Digital

Digital (22, 57, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 57, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(57−35, 57, 257)-Net in Base 32 — Constructive

(22, 57, 257)-net in base 32, using

32¹ times duplication [i] based on (21, 56, 257)-net in base 32, using
- base change [i] based on digital (0, 35, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(57−35, 57, 21015)-Net in Base 32 — Upper bound on s

There is no (22, 57, 21016)-net in base 32, because

1 times m-reduction [i] would yield (22, 56, 21016)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 942824 147570 802966 758265 304631 378182 652399 036724 816244 490435 354032 857786 723388 269197 > 32⁵⁶ [i]