MinT - Best Known (63−24, 63, s)-Nets in Base 32

Best Known (63−24, 63, s)-Nets in Base 32

(63−24, 63, 273)-Net over F₃₂ — Constructive and digital

Digital (39, 63, 273)-net over F₃₂, using

1 times m-reduction [i] based on digital (39, 64, 273)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (5, 13, 77)-net over F₃₂, using
    - (u,Â u+v)-construction [i] based on
      1. digital (0, 4, 33)-net over F₃₂, using
        net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
        Niederreiter sequence [i]
      2. digital (1, 9, 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 (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]
  3. digital (7, 32, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(63−24, 63, 517)-Net in Base 32 — Constructive

(39, 63, 517)-net in base 32, using

1 times m-reduction [i] based on (39, 64, 517)-net in base 32, using
- base change [i] based on digital (15, 40, 517)-net over F₂₅₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (1, 13, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
    2. digital (2, 27, 259)-net over F₂₅₆, using
      - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(63−24, 63, 4047)-Net over F₃₂ — Digital

Digital (39, 63, 4047)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−24, 63, large)-Net in Base 32 — Upper bound on s

There is no (39, 63, large)-net in base 32, because

22 times m-reduction [i] would yield (39, 41, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]