MinT - Information on Result #1231252

Information on Result #1231252

Digital (52, 62, 1693970)-net over F₂₅, using (u,Â u+v)-construction based on

digital (11, 16, 16250)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 650)-net over F₂₅, using
    - s-reduction based on digital (0, 0, s)-net over F₂₅ for arbitrarily large s, using
      - arbitrary set of 25⁰ points [i]
  2. digital (0, 0, 650)-net over F₂₅ (see above)
  3. digital (0, 0, 650)-net over F₂₅ (see above)
  4. digital (0, 0, 650)-net over F₂₅ (see above)
  5. digital (0, 0, 650)-net over F₂₅ (see above)
  6. digital (0, 0, 650)-net over F₂₅ (see above)
  7. digital (0, 0, 650)-net over F₂₅ (see above)
  8. digital (0, 0, 650)-net over F₂₅ (see above)
  9. digital (0, 0, 650)-net over F₂₅ (see above)
  10. digital (0, 0, 650)-net over F₂₅ (see above)
  11. digital (0, 0, 650)-net over F₂₅ (see above)
  12. digital (0, 0, 650)-net over F₂₅ (see above)
  13. digital (0, 0, 650)-net over F₂₅ (see above)
  14. digital (0, 0, 650)-net over F₂₅ (see above)
  15. digital (0, 0, 650)-net over F₂₅ (see above)
  16. digital (0, 0, 650)-net over F₂₅ (see above)
  17. digital (0, 0, 650)-net over F₂₅ (see above)
  18. digital (0, 0, 650)-net over F₂₅ (see above)
  19. digital (0, 0, 650)-net over F₂₅ (see above)
  20. digital (0, 0, 650)-net over F₂₅ (see above)
  21. digital (0, 1, 650)-net over F₂₅, using
    - s-reduction based on digital (0, 1, s)-net over F₂₅ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  22. digital (0, 1, 650)-net over F₂₅ (see above)
  23. digital (0, 1, 650)-net over F₂₅ (see above)
  24. digital (1, 3, 650)-net over F₂₅, using
    - s-reduction based on digital (1, 3, 651)-net over F₂₅, using
      - kÂ =Â 2 construction [i]
  25. digital (5, 10, 650)-net over F₂₅, using
    - generalized (u,Â u+v)-construction [i] based on
      1. digital (0, 0, 26)-net over F₂₅, using
        s-reduction based on digital (0, 0, s)-net over F₂₅ for arbitrarily large s (see above)
      2. digital (0, 0, 26)-net over F₂₅ (see above)
      3. digital (0, 0, 26)-net over F₂₅ (see above)
      4. digital (0, 0, 26)-net over F₂₅ (see above)
      5. digital (0, 0, 26)-net over F₂₅ (see above)
      6. digital (0, 0, 26)-net over F₂₅ (see above)
      7. digital (0, 0, 26)-net over F₂₅ (see above)
      8. digital (0, 0, 26)-net over F₂₅ (see above)
      9. digital (0, 0, 26)-net over F₂₅ (see above)
      10. digital (0, 0, 26)-net over F₂₅ (see above)
      11. digital (0, 0, 26)-net over F₂₅ (see above)
      12. digital (0, 0, 26)-net over F₂₅ (see above)
      13. digital (0, 0, 26)-net over F₂₅ (see above)
      14. digital (0, 0, 26)-net over F₂₅ (see above)
      15. digital (0, 0, 26)-net over F₂₅ (see above)
      16. digital (0, 0, 26)-net over F₂₅ (see above)
      17. digital (0, 0, 26)-net over F₂₅ (see above)
      18. digital (0, 0, 26)-net over F₂₅ (see above)
      19. digital (0, 0, 26)-net over F₂₅ (see above)
      20. digital (0, 0, 26)-net over F₂₅ (see above)
      21. digital (0, 1, 26)-net over F₂₅, using
        s-reduction based on digital (0, 1, s)-net over F₂₅ for arbitrarily large s (see above)
      22. digital (0, 1, 26)-net over F₂₅ (see above)
      23. digital (0, 1, 26)-net over F₂₅ (see above)
      24. digital (0, 2, 26)-net over F₂₅, using
        kÂ =Â 2 construction [i]
      25. digital (0, 5, 26)-net over F₂₅, using
        net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
        Niederreiter sequence [i]
digital (36, 46, 1677720)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁴⁶, 1677720, F₂₅, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(25⁴⁶, 8388600, F₂₅, 10) (dual of [8388600, 8388554, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(25⁴⁶, large, F₂₅, 10) (dual of [large, large−46, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.