MinT - Best Known (29, 69, s)-Nets in Base 32

Best Known (29, 69, s)-Nets in Base 32

(29, 69, 142)-Net over F₃₂ — Constructive and digital

Digital (29, 69, 142)-net over F₃₂, using

2 times m-reduction [i] based on digital (29, 71, 142)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 22, 44)-net over F₃₂, using
    - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
  2. digital (7, 49, 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]

(29, 69, 257)-Net over F₃₂ — Digital

Digital (29, 69, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 69, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(29, 69, 288)-Net in Base 32 — Constructive

(29, 69, 288)-net in base 32, using

1 times m-reduction [i] based on (29, 70, 288)-net in base 32, using
- base change [i] based on digital (9, 50, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(29, 69, 321)-Net in Base 32

(29, 69, 321)-net in base 32, using

3 times m-reduction [i] based on (29, 72, 321)-net in base 32, using
- base change [i] based on digital (2, 45, 321)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(29, 69, 41745)-Net in Base 32 — Upper bound on s

There is no (29, 69, 41746)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 71 699663 834167 631389 357232 797909 490405 193771 292228 527834 300835 601903 309789 643356 233768 357059 244922 034496 > 32⁶⁹ [i]