MinT - Information on Result #1231247

Information on Result #1231247

Digital (50, 61, 1678370)-net over F₂₅, using (u,Â u+v)-construction based on

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, using
      - arbitrary set of 25⁰ points [i]
  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, using
      - construction for strength kÂ =Â 1 [i]
  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 (40, 51, 1677720)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁵¹, 1677720, F₂₅, 11, 11) (dual of [(1677720, 11), 18454869, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(25⁵¹, 8388601, F₂₅, 11) (dual of [8388601, 8388550, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(25⁵¹, large, F₂₅, 11) (dual of [large, large−51, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.