MinT - Information on Result #1230958

Information on Result #1230958

Digital (94, 108, 2397418)-net over F₂₅, using generalized (u,Â u+v)-construction based on

digital (0, 3, 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 (4, 8, 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, 0, 26)-net over F₂₅ (see above)
  22. 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]
  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, 4, 26)-net over F₂₅, using
    - net from sequence [i] based on digital (0, 25)-sequence over F₂₅ (see above)
digital (24, 31, 1198371)-net over F₂₅, using
- s-reduction based on digital (24, 31, 2796200)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25³¹, 2796200, F₂₅, 7, 7) (dual of [(2796200, 7), 19573369, 8]-NRT-code), using
    - OOA 3-folding and stacking with additional row [i] based on linear OA(25³¹, 8388601, F₂₅, 7) (dual of [8388601, 8388570, 8]-code), using
      - discarding factors / shortening the dual code based on linear OA(25³¹, large, F₂₅, 7) (dual of [large, large−31, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 9765626Â | 25¹⁰âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]
digital (52, 66, 1198371)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁶⁶, 1198371, F₂₅, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(25⁶⁶, 8388597, F₂₅, 14) (dual of [8388597, 8388531, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(25⁶⁶, large, F₂₅, 14) (dual of [large, large−66, 15]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [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.