MinT - Best Known (37, 37+53, s)-Nets in Base 32

Best Known (37, 37+53, s)-Nets in Base 32

(37, 37+53, 162)-Net over F₃₂ — Constructive and digital

Digital (37, 90, 162)-net over F₃₂, using

1 times m-reduction [i] based on digital (37, 91, 162)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (3, 30, 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, 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]

(37, 37+53, 273)-Net over F₃₂ — Digital

Digital (37, 90, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 90, 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]

(37, 37+53, 288)-Net in Base 32 — Constructive

(37, 90, 288)-net in base 32, using

8 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
- base change [i] based on digital (9, 70, 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]

(37, 37+53, 342)-Net in Base 32

(37, 90, 342)-net in base 32, using

12 times m-reduction [i] based on (37, 102, 342)-net in base 32, using
- base change [i] based on digital (20, 85, 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]

(37, 37+53, 48312)-Net in Base 32 — Upper bound on s

There is no (37, 90, 48313)-net in base 32, because

1 times m-reduction [i] would yield (37, 89, 48313)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 90 900454 439524 645288 843135 040523 995864 905098 946315 923401 151423 484237 625460 552117 020634 576192 934013 812684 176899 342877 861140 586500 109776 > 32⁸⁹ [i]