Information on Result #548050
There is no linear OA(2570, 148, F25, 67) (dual of [148, 78, 68]-code), because construction Y1 would yield
- OA(2569, 73, S25, 67), but
- the linear programming bound shows that M ≥ 24178 564222 846123 668546 399721 917528 895562 151649 914153 732205 158997 548011 257094 913162 291049 957275 390625 / 7242 > 2569 [i]
- linear OA(2578, 148, F25, 75) (dual of [148, 70, 76]-code), but
- discarding factors / shortening the dual code would yield linear OA(2578, 103, F25, 75) (dual of [103, 25, 76]-code), but
- residual code [i] would yield OA(253, 27, S25, 3), but
- discarding factors / shortening the dual code would yield linear OA(2578, 103, F25, 75) (dual of [103, 25, 76]-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(2571, 149, F25, 68) (dual of [149, 78, 69]-code) | [i] | Truncation | |
| 2 | No linear OA(2572, 150, F25, 69) (dual of [150, 78, 70]-code) | [i] | ||
| 3 | No linear OA(2573, 151, F25, 70) (dual of [151, 78, 71]-code) | [i] | ||
| 4 | No linear OA(2574, 152, F25, 71) (dual of [152, 78, 72]-code) | [i] | ||
| 5 | No linear OA(2575, 153, F25, 72) (dual of [153, 78, 73]-code) | [i] | ||
| 6 | No linear OA(2576, 154, F25, 73) (dual of [154, 78, 74]-code) | [i] | ||
| 7 | No linear OA(2577, 155, F25, 74) (dual of [155, 78, 75]-code) | [i] | ||
| 8 | No linear OOA(2571, 148, F25, 2, 68) (dual of [(148, 2), 225, 69]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(2572, 148, F25, 2, 69) (dual of [(148, 2), 224, 70]-NRT-code) | [i] | ||
| 10 | No linear OOA(2573, 148, F25, 2, 70) (dual of [(148, 2), 223, 71]-NRT-code) | [i] | ||
| 11 | No linear OOA(2574, 148, F25, 2, 71) (dual of [(148, 2), 222, 72]-NRT-code) | [i] | ||
| 12 | No linear OOA(2575, 148, F25, 2, 72) (dual of [(148, 2), 221, 73]-NRT-code) | [i] | ||
| 13 | No linear OOA(2576, 148, F25, 2, 73) (dual of [(148, 2), 220, 74]-NRT-code) | [i] | ||
| 14 | No linear OOA(2577, 148, F25, 2, 74) (dual of [(148, 2), 219, 75]-NRT-code) | [i] | ||
| 15 | No linear OOA(2570, 148, F25, 2, 67) (dual of [(148, 2), 226, 68]-NRT-code) | [i] | Depth Reduction | |
| 16 | No digital (3, 70, 148)-net over F25 | [i] | Extracting Embedded Orthogonal Array | |
| 17 | No linear OA(2594, 164, F25, 90) (dual of [164, 70, 91]-code) | [i] | Construction Y1 (Bound) | |