MinT - Best Known (59, 94, s)-Nets in Base 32

Best Known (59, 94, s)-Nets in Base 32

(59, 94, 350)-Net over F₃₂ — Constructive and digital

Digital (59, 94, 350)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (9, 20, 110)-net over F₃₂, using
  - generalized (u,Â u+v)-construction [i] based on
    1. digital (0, 3, 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 (0, 5, 33)-net over F₃₂, using
      - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
    3. digital (1, 12, 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 (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)

(59, 94, 557)-Net in Base 32 — Constructive

(59, 94, 557)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. digital (1, 18, 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. (41, 76, 513)-net in base 32, using
  - 2 times m-reduction [i] based on (41, 78, 513)-net in base 32, using
    - base change [i] based on digital (28, 65, 513)-net over F₆₄, using
      - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(59, 94, 6347)-Net over F₃₂ — Digital

Digital (59, 94, 6347)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(59, 94, large)-Net in Base 32 — Upper bound on s

There is no (59, 94, large)-net in base 32, because

33 times m-reduction [i] would yield (59, 61, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]