MinT - Best Known (47, 47+29, s)-Nets in Base 32

Best Known (47, 47+29, s)-Nets in Base 32

(47, 47+29, 306)-Net over F₃₂ — Constructive and digital

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, 47+29, 517)-Net in Base 32 — Constructive

(47, 76, 517)-net in base 32, using

1 times m-reduction [i] based on (47, 77, 517)-net in base 32, using
- base change [i] based on (25, 55, 517)-net in base 128, using
  - 1 times m-reduction [i] based on (25, 56, 517)-net in base 128, using
    - base change [i] based on digital (18, 49, 517)-net over F₂₅₆, using
      - (u,Â u+v)-construction [i] based on
        digital (1, 16, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
        digital (2, 33, 259)-net over F₂₅₆, using
        net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(47, 47+29, 4451)-Net over F₃₂ — Digital

Digital (47, 76, 4451)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(47, 47+29, large)-Net in Base 32 — Upper bound on s

There is no (47, 76, large)-net in base 32, because

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