MinT - Best Known (40, 87, s)-Nets in Base 32

Best Known (40, 87, s)-Nets in Base 32

(40, 87, 202)-Net over F₃₂ — Constructive and digital

Digital (40, 87, 202)-net over F₃₂, using

1 times m-reduction [i] based on digital (40, 88, 202)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 31, 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]
  2. digital (9, 57, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(40, 87, 288)-Net in Base 32 — Constructive

(40, 87, 288)-net in base 32, using

21 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
- base change [i] based on (22, 90, 288)-net in base 64, using
  - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
    - base change [i] based on digital (9, 78, 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]

(40, 87, 409)-Net over F₃₂ — Digital

Digital (40, 87, 409)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 87, 129124)-Net in Base 32 — Upper bound on s

There is no (40, 87, 129125)-net in base 32, because

1 times m-reduction [i] would yield (40, 86, 129125)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2773 131664 943386 618416 323771 101547 686792 018746 931877 653594 284941 185999 709716 781849 966805 101730 921332 163193 722233 185332 407147 262176 > 32⁸⁶ [i]