MinT - Best Known (36, 36+59, s)-Nets in Base 32

Best Known (36, 36+59, s)-Nets in Base 32

(36, 36+59, 131)-Net over F₃₂ — Constructive and digital

Digital (36, 95, 131)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 29, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
      - the rational function field F₃₂(x) [i]
    - Niederreiter sequence [i]
2. digital (7, 66, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(36, 36+59, 257)-Net in Base 32 — Constructive

(36, 95, 257)-net in base 32, using

1 times m-reduction [i] based on (36, 96, 257)-net in base 32, using
- base change [i] based on digital (0, 60, 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]

(36, 36+59, 273)-Net over F₃₂ — Digital

Digital (36, 95, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 95, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(36, 36+59, 342)-Net in Base 32

(36, 95, 342)-net in base 32, using

1 times m-reduction [i] based on (36, 96, 342)-net in base 32, using
- base change [i] based on digital (20, 80, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(36, 36+59, 28463)-Net in Base 32 — Upper bound on s

There is no (36, 95, 28464)-net in base 32, because

1 times m-reduction [i] would yield (36, 94, 28464)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3048 866077 173012 983665 221266 953057 071207 724182 286151 241447 009688 483851 942747 407517 626077 107158 318430 896197 565560 045034 804063 203580 956140 632790 > 32⁹⁴ [i]