MinT - Best Known (57, 57+34, s)-Nets in Base 32

Best Known (57, 57+34, s)-Nets in Base 32

(57, 57+34, 338)-Net over F₃₂ — Constructive and digital

Digital (57, 91, 338)-net over F₃₂, using

1 times m-reduction [i] based on digital (57, 92, 338)-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 (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)

(57, 57+34, 547)-Net in Base 32 — Constructive

(57, 91, 547)-net in base 32, using

base change [i] based on (31, 65, 547)-net in base 128, using
- (u,Â u+v)-construction [i] based on
  1. (5, 22, 259)-net in base 128, using
    - 2 times m-reduction [i] based on (5, 24, 259)-net in base 128, using
      - base change [i] based on digital (2, 21, 259)-net over F₂₅₆, using
        net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. digital (9, 43, 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]

(57, 57+34, 6022)-Net over F₃₂ — Digital

Digital (57, 91, 6022)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(57, 57+34, large)-Net in Base 32 — Upper bound on s

There is no (57, 91, large)-net in base 32, because

32 times m-reduction [i] would yield (57, 59, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]