MinT - Best Known (56−35, 56, s)-Nets in Base 32

Best Known (56−35, 56, s)-Nets in Base 32

(56−35, 56, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 56, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 56, 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]

(56−35, 56, 185)-Net over F₃₂ — Digital

Digital (21, 56, 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]

(56−35, 56, 257)-Net in Base 32 — Constructive

(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]

(56−35, 56, 17138)-Net in Base 32 — Upper bound on s

There is no (21, 56, 17139)-net in base 32, because

1 times m-reduction [i] would yield (21, 55, 17139)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 60745 553627 361181 073235 743041 552637 427609 634043 154065 870746 427429 345241 340278 616042 > 32⁵⁵ [i]