MinT - Best Known (52, 52+35, s)-Nets in Base 32

Best Known (52, 52+35, s)-Nets in Base 32

(52, 52+35, 300)-Net over F₃₂ — Constructive and digital

Digital (52, 87, 300)-net over F₃₂, using

32¹ times duplication [i] based on digital (51, 86, 300)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 18, 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 (7, 24, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (9, 44, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(52, 52+35, 515)-Net in Base 32 — Constructive

(52, 87, 515)-net in base 32, using

1 times m-reduction [i] based on (52, 88, 515)-net in base 32, using
- base change [i] based on digital (19, 55, 515)-net over F₂₅₆, using
  - (u,Â u+v)-construction [i] based on
    1. digital (0, 18, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]
    2. digital (1, 37, 258)-net over F₂₅₆, using
      - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]

(52, 52+35, 3118)-Net over F₃₂ — Digital

Digital (52, 87, 3118)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+35, large)-Net in Base 32 — Upper bound on s

There is no (52, 87, large)-net in base 32, because

33 times m-reduction [i] would yield (52, 54, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]