MinT - Best Known (63, 63+41, s)-Nets in Base 32

Best Known (63, 63+41, s)-Nets in Base 32

(63, 63+41, 338)-Net over F₃₂ — Constructive and digital

Digital (63, 104, 338)-net over F₃₂, using

32¹ times duplication [i] based on digital (62, 103, 338)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 20, 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]
  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)

(63, 63+41, 557)-Net in Base 32 — Constructive

(63, 104, 557)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. digital (1, 21, 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. (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]

(63, 63+41, 4187)-Net over F₃₂ — Digital

Digital (63, 104, 4187)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+41, large)-Net in Base 32 — Upper bound on s

There is no (63, 104, large)-net in base 32, because

39 times m-reduction [i] would yield (63, 65, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]