MinT - Best Known (32, 75, s)-Nets in Base 32

Best Known (32, 75, s)-Nets in Base 32

(32, 75, 162)-Net over F₃₂ — Constructive and digital

Digital (32, 75, 162)-net over F₃₂, using

1 times m-reduction [i] based on digital (32, 76, 162)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (3, 25, 64)-net over F₃₂, using
    - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]
  2. digital (7, 51, 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]

(32, 75, 273)-Net over F₃₂ — Digital

Digital (32, 75, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 75, 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]

(32, 75, 288)-Net in Base 32 — Constructive

(32, 75, 288)-net in base 32, using

t-expansion [i] based on (31, 75, 288)-net in base 32, using
- 2 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
  - base change [i] based on digital (9, 55, 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]

(32, 75, 321)-Net in Base 32

(32, 75, 321)-net in base 32, using

5 times m-reduction [i] based on (32, 80, 321)-net in base 32, using
- base change [i] based on digital (2, 50, 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]

(32, 75, 56352)-Net in Base 32 — Upper bound on s

There is no (32, 75, 56353)-net in base 32, because

1 times m-reduction [i] would yield (32, 74, 56353)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2405 677024 971193 540643 376266 122408 716264 192307 417446 064137 346531 176716 297369 987474 457480 004328 943061 102825 499424 > 32⁷⁴ [i]