MinT - Best Known (56, 56+36, s)-Nets in Base 32

Best Known (56, 56+36, s)-Nets in Base 32

(56, 56+36, 316)-Net over F₃₂ — Constructive and digital

Digital (56, 92, 316)-net over F₃₂, using

2 times m-reduction [i] based on digital (56, 94, 316)-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 (7, 26, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  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]

(56, 56+36, 516)-Net in Base 32 — Constructive

(56, 92, 516)-net in base 32, using

1 times m-reduction [i] based on (56, 93, 516)-net in base 32, using
- (u,Â u+v)-construction [i] based on
  1. (13, 31, 258)-net in base 32, using
    - 1 times m-reduction [i] based on (13, 32, 258)-net in base 32, using
      - base change [i] based on digital (1, 20, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
  2. (25, 62, 258)-net in base 32, using
    - 2 times m-reduction [i] based on (25, 64, 258)-net in base 32, using
      - base change [i] based on digital (1, 40, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(56, 56+36, 4075)-Net over F₃₂ — Digital

Digital (56, 92, 4075)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(56, 56+36, large)-Net in Base 32 — Upper bound on s

There is no (56, 92, large)-net in base 32, because

34 times m-reduction [i] would yield (56, 58, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]