MinT - Best Known (65, 65+37, s)-Nets in Base 32

Best Known (65, 65+37, s)-Nets in Base 32

(65, 65+37, 371)-Net over F₃₂ — Constructive and digital

Digital (65, 102, 371)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (5, 14, 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, 10, 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, 25, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
4. digital (7, 44, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(65, 65+37, 593)-Net in Base 32 — Constructive

(65, 102, 593)-net in base 32, using

base change [i] based on digital (48, 85, 593)-net over F₆₄, using
- 1 times m-reduction [i] based on digital (48, 86, 593)-net over F₆₄, using
  - (u,Â u+v)-construction [i] based on
    1. digital (1, 20, 80)-net over F₆₄, using
      - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
    2. digital (28, 66, 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]

(65, 65+37, 8490)-Net over F₃₂ — Digital

Digital (65, 102, 8490)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+37, large)-Net in Base 32 — Upper bound on s

There is no (65, 102, large)-net in base 32, because

35 times m-reduction [i] would yield (65, 67, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]