Information on Result #548058
There is no linear OA(3288, 187, F32, 85) (dual of [187, 99, 86]-code), because construction Y1 would yield
- OA(3287, 91, S32, 85), but
- the linear programming bound shows that M ≥ 3218 248804 644806 290772 103657 191613 826913 486259 137011 802066 676331 137713 410455 220883 164990 453062 699224 855954 368127 744971 436177 620882 948096 / 34443 > 3287 [i]
- linear OA(3299, 187, F32, 96) (dual of [187, 88, 97]-code), but
- discarding factors / shortening the dual code would yield linear OA(3299, 132, F32, 96) (dual of [132, 33, 97]-code), but
- residual code [i] would yield OA(323, 35, S32, 3), but
- 1 times truncation [i] would yield OA(322, 34, S32, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 1055 > 322 [i]
- 1 times truncation [i] would yield OA(322, 34, S32, 2), but
- residual code [i] would yield OA(323, 35, S32, 3), but
- discarding factors / shortening the dual code would yield linear OA(3299, 132, F32, 96) (dual of [132, 33, 97]-code), but
Mode: Bound (linear).
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3289, 188, F32, 86) (dual of [188, 99, 87]-code) | [i] | Truncation | |
| 2 | No linear OA(3290, 189, F32, 87) (dual of [189, 99, 88]-code) | [i] | ||
| 3 | No linear OA(3291, 190, F32, 88) (dual of [190, 99, 89]-code) | [i] | ||
| 4 | No linear OA(3292, 191, F32, 89) (dual of [191, 99, 90]-code) | [i] | ||
| 5 | No linear OA(3293, 192, F32, 90) (dual of [192, 99, 91]-code) | [i] | ||
| 6 | No linear OA(3294, 193, F32, 91) (dual of [193, 99, 92]-code) | [i] | ||
| 7 | No linear OA(3295, 194, F32, 92) (dual of [194, 99, 93]-code) | [i] | ||
| 8 | No linear OA(3296, 195, F32, 93) (dual of [195, 99, 94]-code) | [i] | ||
| 9 | No linear OA(3297, 196, F32, 94) (dual of [196, 99, 95]-code) | [i] | ||
| 10 | No linear OA(3298, 197, F32, 95) (dual of [197, 99, 96]-code) | [i] | ||
| 11 | No linear OOA(3289, 187, F32, 2, 86) (dual of [(187, 2), 285, 87]-NRT-code) | [i] | m-Reduction for OOAs | |
| 12 | No linear OOA(3290, 187, F32, 2, 87) (dual of [(187, 2), 284, 88]-NRT-code) | [i] | ||
| 13 | No linear OOA(3291, 187, F32, 2, 88) (dual of [(187, 2), 283, 89]-NRT-code) | [i] | ||
| 14 | No linear OOA(3292, 187, F32, 2, 89) (dual of [(187, 2), 282, 90]-NRT-code) | [i] | ||
| 15 | No linear OOA(3293, 187, F32, 2, 90) (dual of [(187, 2), 281, 91]-NRT-code) | [i] | ||
| 16 | No linear OOA(3294, 187, F32, 2, 91) (dual of [(187, 2), 280, 92]-NRT-code) | [i] | ||
| 17 | No linear OOA(3295, 187, F32, 2, 92) (dual of [(187, 2), 279, 93]-NRT-code) | [i] | ||
| 18 | No linear OOA(3296, 187, F32, 2, 93) (dual of [(187, 2), 278, 94]-NRT-code) | [i] | ||
| 19 | No linear OOA(3297, 187, F32, 2, 94) (dual of [(187, 2), 277, 95]-NRT-code) | [i] | ||
| 20 | No linear OOA(3298, 187, F32, 2, 95) (dual of [(187, 2), 276, 96]-NRT-code) | [i] | ||
| 21 | No linear OOA(3288, 187, F32, 2, 85) (dual of [(187, 2), 286, 86]-NRT-code) | [i] | Depth Reduction | |
| 22 | No digital (3, 88, 187)-net over F32 | [i] | Extracting Embedded Orthogonal Array | |