MinT - Best Known (89−34, 89, s)-Nets in Base 32

Best Known (89−34, 89, s)-Nets in Base 32

(89−34, 89, 322)-Net over F₃₂ — Constructive and digital

Digital (55, 89, 322)-net over F₃₂, using

1 times m-reduction [i] based on digital (55, 90, 322)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 18, 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, 26, 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, 46, 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]

(89−34, 89, 545)-Net in Base 32 — Constructive

(55, 89, 545)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (11, 28, 257)-net in base 32, using
  - base change [i] based on (3, 20, 257)-net in base 128, using
    - 4 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
      - base change [i] based on digital (0, 21, 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. (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]

(89−34, 89, 4884)-Net over F₃₂ — Digital

Digital (55, 89, 4884)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(89−34, 89, large)-Net in Base 32 — Upper bound on s

There is no (55, 89, large)-net in base 32, because

32 times m-reduction [i] would yield (55, 57, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]