MinT - Information on Result #1197232

Information on Result #1197232

Digital (11, 16, 20411)-net over F₂₇, using net defined by OOA based on linear OOA(27¹⁶, 20411, F₂₇, 6, 5) (dual of [(20411, 6), 122450, 6]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(27¹⁶, 20412, F₂₇, 2, 5) (dual of [(20412, 2), 40808, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27⁰, s, F₂₇, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  3. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  4. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  5. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  6. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  7. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  8. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  9. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  10. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  11. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  12. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  13. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  14. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  15. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  16. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  17. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  18. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  19. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  20. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  21. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  22. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  23. linear OOA(27¹, 756, F₂₇, 2, 1) (dual of [(756, 2), 1511, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27¹, s, F₂₇, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  24. linear OOA(27¹, 756, F₂₇, 2, 1) (dual of [(756, 2), 1511, 2]-NRT-code) (see above)
  25. linear OOA(27¹, 756, F₂₇, 2, 1) (dual of [(756, 2), 1511, 2]-NRT-code) (see above)
  26. linear OOA(27³, 756, F₂₇, 2, 2) (dual of [(756, 2), 1509, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27³, 757, F₂₇, 2, 2) (dual of [(757, 2), 1511, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(27³, 757, F₂₇, 2) (dual of [757, 754, 3]-code), using
        Hamming code H(3,27) [i]
  27. linear OOA(27¹⁰, 756, F₂₇, 2, 5) (dual of [(756, 2), 1502, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(27⁰, s, F₂₇, 2, 0) for arbitrarily large s (see above)
      2. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      3. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      4. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      5. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      6. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      7. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      8. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      9. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      10. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      11. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      12. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      13. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      14. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      15. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      16. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      17. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      18. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      19. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      20. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      21. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      22. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      23. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(27¹, s, F₂₇, 2, 1) for arbitrarily large s (see above)
      24. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
      25. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
      26. linear OOA(27², 28, F₂₇, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;54,27) [i]
      27. linear OOA(27⁵, 28, F₂₇, 2, 5) (dual of [(28, 2), 51, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;51,27) [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

The following results depend on this result:

	Result		This result only	Method
1	Digital (52, 62, 1698131)-net over F₂₇	[i]		(u,Â u+v)-Construction for Nets
2	Digital (56, 67, 1698131)-net over F₂₇	[i]		(u,Â u+v)-Construction for Nets