MinT - Best Known (38, 38+25, s)-Nets in Base 32

Best Known (38, 38+25, s)-Nets in Base 32

(38, 38+25, 262)-Net over F₃₂ — Constructive and digital

Digital (38, 63, 262)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (4, 12, 66)-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 (0, 8, 33)-net over F₃₂, using
      - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
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, 32, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(38, 38+25, 516)-Net in Base 32 — Constructive

(38, 63, 516)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (9, 21, 258)-net in base 32, using
  - base change [i] based on (3, 15, 258)-net in base 128, using
    - 1 times m-reduction [i] based on (3, 16, 258)-net in base 128, using
      - base change [i] based on digital (1, 14, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
2. (17, 42, 258)-net in base 32, using
  - base change [i] based on (10, 35, 258)-net in base 64, using
    - 1 times m-reduction [i] based on (10, 36, 258)-net in base 64, using
      - base change [i] based on digital (1, 27, 258)-net over F₂₅₆, using
        net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆ (see above)

(38, 38+25, 2837)-Net over F₃₂ — Digital

Digital (38, 63, 2837)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+25, large)-Net in Base 32 — Upper bound on s

There is no (38, 63, large)-net in base 32, because

23 times m-reduction [i] would yield (38, 40, large)-net in base 32, but
- mutually orthogonal hypercube bound [i]