MinT - Best Known (38, 38+23, s)-Nets in Base 32

Best Known (38, 38+23, s)-Nets in Base 32

(38, 38+23, 308)-Net over F₃₂ — Constructive and digital

Digital (38, 61, 308)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 2, 33)-net over F₃₂, using
  - kÂ =Â 2 construction [i]
2. digital (0, 2, 33)-net over F₃₂ (see above)
3. digital (0, 3, 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]
4. digital (0, 3, 33)-net over F₃₂ (see above)
5. digital (0, 4, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
6. digital (0, 5, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
7. digital (0, 7, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
8. digital (0, 11, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂ (see above)
9. digital (1, 24, 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]

(38, 38+23, 518)-Net in Base 32 — Constructive

(38, 61, 518)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (10, 21, 259)-net in base 32, using
  - base change [i] based on (4, 15, 259)-net in base 128, using
    - 1 times m-reduction [i] based on (4, 16, 259)-net in base 128, using
      - base change [i] based on digital (2, 14, 259)-net over F₂₅₆, using
        net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
        Niederreiter sequence [i]
2. (17, 40, 259)-net in base 32, using
  - base change [i] based on digital (2, 25, 259)-net over F₂₅₆, using
    - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆ (see above)

(38, 38+23, 4365)-Net over F₃₂ — Digital

Digital (38, 61, 4365)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 38+23, large)-Net in Base 32 — Upper bound on s

There is no (38, 61, large)-net in base 32, because

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