MinT - Information on Result #1232974

Information on Result #1232974

Digital (51, 61, 1687953)-net over F₂₇, using (u,Â u+v)-construction based on

digital (10, 15, 10233)-net over F₂₇, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 379)-net over F₂₇, using
    - s-reduction based on digital (0, 0, s)-net over F₂₇ for arbitrarily large s, using
      - arbitrary set of 27⁰ points [i]
  2. digital (0, 0, 379)-net over F₂₇ (see above)
  3. digital (0, 0, 379)-net over F₂₇ (see above)
  4. digital (0, 0, 379)-net over F₂₇ (see above)
  5. digital (0, 0, 379)-net over F₂₇ (see above)
  6. digital (0, 0, 379)-net over F₂₇ (see above)
  7. digital (0, 0, 379)-net over F₂₇ (see above)
  8. digital (0, 0, 379)-net over F₂₇ (see above)
  9. digital (0, 0, 379)-net over F₂₇ (see above)
  10. digital (0, 0, 379)-net over F₂₇ (see above)
  11. digital (0, 0, 379)-net over F₂₇ (see above)
  12. digital (0, 0, 379)-net over F₂₇ (see above)
  13. digital (0, 0, 379)-net over F₂₇ (see above)
  14. digital (0, 0, 379)-net over F₂₇ (see above)
  15. digital (0, 0, 379)-net over F₂₇ (see above)
  16. digital (0, 0, 379)-net over F₂₇ (see above)
  17. digital (0, 0, 379)-net over F₂₇ (see above)
  18. digital (0, 0, 379)-net over F₂₇ (see above)
  19. digital (0, 0, 379)-net over F₂₇ (see above)
  20. digital (0, 0, 379)-net over F₂₇ (see above)
  21. digital (0, 0, 379)-net over F₂₇ (see above)
  22. digital (0, 0, 379)-net over F₂₇ (see above)
  23. digital (0, 1, 379)-net over F₂₇, using
    - s-reduction based on digital (0, 1, s)-net over F₂₇ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  24. digital (0, 1, 379)-net over F₂₇ (see above)
  25. digital (0, 1, 379)-net over F₂₇ (see above)
  26. digital (1, 3, 379)-net over F₂₇, using
    - s-reduction based on digital (1, 3, 757)-net over F₂₇, using
      - kÂ =Â 2 construction [i]
  27. digital (4, 9, 379)-net over F₂₇, using
    - (u,Â u+v)-construction [i] based on
      1. digital (0, 2, 28)-net over F₂₇, using
        kÂ =Â 2 construction [i]
      2. digital (2, 7, 351)-net over F₂₇, using
        net defined by OOA [i] based on linear OOA(27⁷, 351, F₂₇, 5, 5) (dual of [(351, 5), 1748, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(27⁷, 703, F₂₇, 5) (dual of [703, 696, 6]-code), using
        a code by Danev and Olsson [i]
digital (36, 46, 1677720)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁴⁶, 1677720, F₂₇, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
  - OA 5-folding and stacking [i] based on linear OA(27⁴⁶, 8388600, F₂₇, 10) (dual of [8388600, 8388554, 11]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁴⁶, large, F₂₇, 10) (dual of [large, large−46, 11]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’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.