Information on Result #1208072
Digital (223, 235, 6990613)-net over F3, using (u, u+v)-construction based on
- digital (61, 67, 2796313)-net over F3, using
- net defined by OOA [i] based on linear OOA(367, 2796313, F3, 6, 6) (dual of [(2796313, 6), 16777811, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(367, 2796313, F3, 5, 6) (dual of [(2796313, 5), 13981498, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(37, 112, F3, 5, 3) (dual of [(112, 5), 553, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(37, 112, F3, 3, 3) (dual of [(112, 3), 329, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(37, 112, F3, 2, 3) (dual of [(112, 2), 217, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(37, 112, F3, 3, 3) (dual of [(112, 3), 329, 4]-NRT-code), using
- linear OOA(360, 2796201, F3, 5, 6) (dual of [(2796201, 5), 13980945, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(360, large, F3, 6) (dual of [large, large−60, 7]-code), using
- linear OOA(37, 112, F3, 5, 3) (dual of [(112, 5), 553, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(367, 2796313, F3, 5, 6) (dual of [(2796313, 5), 13981498, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(367, 2796313, F3, 6, 6) (dual of [(2796313, 6), 16777811, 7]-NRT-code), using
- digital (156, 168, 4194300)-net over F3, using
- trace code for nets [i] based on digital (44, 56, 1398100)-net over F27, using
- net defined by OOA [i] based on linear OOA(2756, 1398100, F27, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2756, 8388600, F27, 12) (dual of [8388600, 8388544, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 275−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2756, large, F27, 12) (dual of [large, large−56, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2756, 8388600, F27, 12) (dual of [8388600, 8388544, 13]-code), using
- net defined by OOA [i] based on linear OOA(2756, 1398100, F27, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- trace code for nets [i] based on digital (44, 56, 1398100)-net over F27, using
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 | Linear OOA(3235, 6990613, F3, 5, 12) (dual of [(6990613, 5), 34952830, 13]-NRT-code) | [i] | Extracting Embedded OOA | |