MinT - Best Known (35, 35+52, s)-Nets in Base 32

Best Known (35, 35+52, s)-Nets in Base 32

(35, 35+52, 142)-Net over F₃₂ — Constructive and digital

Digital (35, 87, 142)-net over F₃₂, using

2 times m-reduction [i] based on digital (35, 89, 142)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 28, 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, 61, 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]

(35, 35+52, 273)-Net over F₃₂ — Digital

Digital (35, 87, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 87, 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]

(35, 35+52, 288)-Net in Base 32 — Constructive

(35, 87, 288)-net in base 32, using

4 times m-reduction [i] based on (35, 91, 288)-net in base 32, using
- base change [i] based on digital (9, 65, 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]

(35, 35+52, 342)-Net in Base 32

(35, 87, 342)-net in base 32, using

3 times m-reduction [i] based on (35, 90, 342)-net in base 32, using
- base change [i] based on digital (20, 75, 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]

(35, 35+52, 37003)-Net in Base 32 — Upper bound on s

There is no (35, 87, 37004)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 88780 932867 507481 099732 838826 279919 410025 075837 345487 756755 391740 628676 351274 573864 171682 612501 186002 452984 676751 203289 890412 139800 > 32⁸⁷ [i]