MinT - Best Known (58, 58+37, s)-Nets in Base 32

Best Known (58, 58+37, s)-Nets in Base 32

(58, 58+37, 322)-Net over F₃₂ — Constructive and digital

Digital (58, 95, 322)-net over F₃₂, using

1 times m-reduction [i] based on digital (58, 96, 322)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 19, 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, 28, 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]
  3. digital (11, 49, 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]

(58, 58+37, 545)-Net in Base 32 — Constructive

(58, 95, 545)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (12, 30, 257)-net in base 32, using
  - 2 times m-reduction [i] based on (12, 32, 257)-net in base 32, using
    - base change [i] based on digital (0, 20, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
2. (28, 65, 288)-net in base 32, using
  - 1 times m-reduction [i] based on (28, 66, 288)-net in base 32, using
    - base change [i] based on (17, 55, 288)-net in base 64, using
      - 1 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
        base change [i] based on digital (9, 48, 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]

(58, 58+37, 4336)-Net over F₃₂ — Digital

Digital (58, 95, 4336)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(58, 58+37, large)-Net in Base 32 — Upper bound on s

There is no (58, 95, large)-net in base 32, because

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