MinT - Best Known (92−34, 92, s)-Nets in Base 32

Best Known (92−34, 92, s)-Nets in Base 32

(92−34, 92, 339)-Net over F₃₂ — Constructive and digital

Digital (58, 92, 339)-net over F₃₂, using

1 times m-reduction [i] based on digital (58, 93, 339)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (8, 19, 99)-net over F₃₂, using
    - generalized (u,Â u+v)-construction [i] based on
      1. digital (0, 3, 33)-net over F₃₂, using
        net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
        Niederreiter sequence [i]
      2. digital (0, 5, 33)-net over F₃₂, using
        net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
      3. digital (0, 11, 33)-net over F₃₂, using
        net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
  2. digital (11, 28, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]
  3. digital (11, 46, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(92−34, 92, 547)-Net in Base 32 — Constructive

(58, 92, 547)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (14, 31, 259)-net in base 32, using
  - 1 times m-reduction [i] based on (14, 32, 259)-net in base 32, using
    - base change [i] based on digital (2, 20, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
2. (27, 61, 288)-net in base 32, using
  - 2 times m-reduction [i] based on (27, 63, 288)-net in base 32, using
    - base change [i] based on digital (9, 45, 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]

(92−34, 92, 6687)-Net over F₃₂ — Digital

Digital (58, 92, 6687)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−34, 92, large)-Net in Base 32 — Upper bound on s

There is no (58, 92, large)-net in base 32, because

32 times m-reduction [i] would yield (58, 60, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]