MinT - Best Known (47, 75, s)-Nets in Base 32

Best Known (47, 75, s)-Nets in Base 32

(47, 75, 306)-Net over F₃₂ — Constructive and digital

Digital (47, 75, 306)-net over F₃₂, using

1 times m-reduction [i] based on digital (47, 76, 306)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (6, 15, 88)-net over F₃₂, using
    - (u,Â u+v)-construction [i] based on
      1. digital (1, 5, 44)-net over F₃₂, using
        net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
      2. digital (1, 10, 44)-net over F₃₂, using
        net from sequence [i] based on digital (1, 43)-sequence over F₃₂ (see above)
  2. digital (7, 21, 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]
  3. digital (11, 40, 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]

(47, 75, 518)-Net in Base 32 — Constructive

(47, 75, 518)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (13, 27, 259)-net in base 32, using
  - 1 times m-reduction [i] based on (13, 28, 259)-net in base 32, using
    - base change [i] based on (5, 20, 259)-net in base 128, using
      - 4 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. (20, 48, 259)-net in base 32, using
  - base change [i] based on digital (2, 30, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(47, 75, 5359)-Net over F₃₂ — Digital

Digital (47, 75, 5359)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 75, large)-Net in Base 32 — Upper bound on s

There is no (47, 75, large)-net in base 32, because

26 times m-reduction [i] would yield (47, 49, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]