MinT - Best Known (52, 52+30, s)-Nets in Base 32

Best Known (52, 52+30, s)-Nets in Base 32

(52, 52+30, 324)-Net over F₃₂ — Constructive and digital

Digital (52, 82, 324)-net over F₃₂, using

1 times m-reduction [i] based on digital (52, 83, 324)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (3, 10, 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 (3, 13, 64)-net over F₃₂, using
    - net from sequence [i] based on digital (3, 63)-sequence over F₃₂ (see above)
  3. digital (7, 22, 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]
  4. digital (7, 38, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(52, 52+30, 546)-Net in Base 32 — Constructive

(52, 82, 546)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (12, 27, 258)-net in base 32, using
  - 1 times m-reduction [i] based on (12, 28, 258)-net in base 32, using
    - base change [i] based on (4, 20, 258)-net in base 128, using
      - 4 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
        base change [i] based on digital (1, 21, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
2. (25, 55, 288)-net in base 32, using
  - 1 times m-reduction [i] based on (25, 56, 288)-net in base 32, using
    - base change [i] based on digital (9, 40, 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]

(52, 52+30, 6802)-Net over F₃₂ — Digital

Digital (52, 82, 6802)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+30, large)-Net in Base 32 — Upper bound on s

There is no (52, 82, large)-net in base 32, because

28 times m-reduction [i] would yield (52, 54, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]