MinT - Best Known (65, 65+41, s)-Nets in Base 32

Best Known (65, 65+41, s)-Nets in Base 32

(65, 65+41, 348)-Net over F₃₂ — Constructive and digital

Digital (65, 106, 348)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (10, 23, 108)-net over F₃₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (1, 7, 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 (3, 16, 64)-net over F₃₂, using
      - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]
2. digital (11, 31, 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, 52, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(65, 65+41, 577)-Net in Base 32 — Constructive

(65, 106, 577)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. digital (3, 23, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. (42, 83, 513)-net in base 32, using
  - 1 times m-reduction [i] based on (42, 84, 513)-net in base 32, using
    - base change [i] based on digital (28, 70, 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+41, 4975)-Net over F₃₂ — Digital

Digital (65, 106, 4975)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+41, large)-Net in Base 32 — Upper bound on s

There is no (65, 106, large)-net in base 32, because

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