Information on Result #547688
There is no linear OA(2128, 181, F2, 60) (dual of [181, 53, 61]-code), because construction Y1 would yield
- linear OA(2127, 161, F2, 60) (dual of [161, 34, 61]-code), but
- construction Y1 [i] would yield
- OA(2126, 149, S2, 60), but
- the linear programming bound shows that M ≥ 40 354766 457887 934259 048521 444548 255732 989952 / 438495 > 2126 [i]
- OA(234, 161, S2, 12), but
- discarding factors would yield OA(234, 154, S2, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 17486 314616 > 234 [i]
- discarding factors would yield OA(234, 154, S2, 12), but
- OA(2126, 149, S2, 60), but
- construction Y1 [i] would yield
- OA(253, 181, S2, 20), but
- discarding factors would yield OA(253, 180, S2, 20), but
- the linear programming bound shows that M ≥ 2 488754 712874 464491 680229 064205 986311 441557 225472 / 271 456013 974306 311726 277255 439899 > 253 [i]
- discarding factors would yield OA(253, 180, S2, 20), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2129, 182, F2, 61) (dual of [182, 53, 62]-code) | [i] | Truncation | |
| 2 | No linear OOA(2129, 181, F2, 2, 61) (dual of [(181, 2), 233, 62]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(2128, 181, F2, 2, 60) (dual of [(181, 2), 234, 61]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(2128, 181, F2, 3, 60) (dual of [(181, 3), 415, 61]-NRT-code) | [i] | ||
| 5 | No linear OOA(2128, 181, F2, 4, 60) (dual of [(181, 4), 596, 61]-NRT-code) | [i] | ||
| 6 | No linear OOA(2128, 181, F2, 5, 60) (dual of [(181, 5), 777, 61]-NRT-code) | [i] | ||
| 7 | No linear OOA(2128, 181, F2, 6, 60) (dual of [(181, 6), 958, 61]-NRT-code) | [i] | ||
| 8 | No linear OOA(2128, 181, F2, 7, 60) (dual of [(181, 7), 1139, 61]-NRT-code) | [i] | ||
| 9 | No linear OOA(2128, 181, F2, 8, 60) (dual of [(181, 8), 1320, 61]-NRT-code) | [i] | ||
| 10 | No digital (68, 128, 181)-net over F2 | [i] | Extracting Embedded Orthogonal Array | |