MinT - Best Known (37, 37+54, s)-Nets in Base 32

Best Known (37, 37+54, s)-Nets in Base 32

(37, 37+54, 162)-Net over F₃₂ — Constructive and digital

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+54, 273)-Net over F₃₂ — Digital

Digital (37, 91, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 91, 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+54, 288)-Net in Base 32 — Constructive

(37, 91, 288)-net in base 32, using

7 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+54, 342)-Net in Base 32

(37, 91, 342)-net in base 32, using

11 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+54, 41669)-Net in Base 32 — Upper bound on s

There is no (37, 91, 41670)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93093 598147 116564 684146 266760 919893 148514 724119 069497 347000 308064 597059 069141 250905 908794 548496 577642 924568 733315 812649 146065 912518 565648 > 32⁹¹ [i]