Information on Result #548626
There is no linear OA(4240, 252, F4, 180) (dual of [252, 12, 181]-code), because construction Y1 would yield
- linear OA(4239, 246, F4, 180) (dual of [246, 7, 181]-code), but
- residual code [i] would yield linear OA(459, 65, F4, 45) (dual of [65, 6, 46]-code), but
- 1 times truncation [i] would yield linear OA(458, 64, F4, 44) (dual of [64, 6, 45]-code), but
- residual code [i] would yield linear OA(414, 19, F4, 11) (dual of [19, 5, 12]-code), but
- 1 times truncation [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- “Liz†bound on codes from Brouwer’s database [i]
- 1 times truncation [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- residual code [i] would yield linear OA(414, 19, F4, 11) (dual of [19, 5, 12]-code), but
- 1 times truncation [i] would yield linear OA(458, 64, F4, 44) (dual of [64, 6, 45]-code), but
- residual code [i] would yield linear OA(459, 65, F4, 45) (dual of [65, 6, 46]-code), but
- OA(412, 252, S4, 6), but
- discarding factors would yield OA(412, 156, S4, 6), but
- the Rao or (dual) Hamming bound shows that M ≥ 16 866019 > 412 [i]
- discarding factors would yield OA(412, 156, S4, 6), 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(4241, 253, F4, 181) (dual of [253, 12, 182]-code) | [i] | Truncation | |
| 2 | No linear OA(4242, 254, F4, 182) (dual of [254, 12, 183]-code) | [i] | ||
| 3 | No linear OA(4243, 255, F4, 183) (dual of [255, 12, 184]-code) | [i] | ||
| 4 | No linear OOA(4241, 252, F4, 2, 181) (dual of [(252, 2), 263, 182]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4242, 252, F4, 2, 182) (dual of [(252, 2), 262, 183]-NRT-code) | [i] | ||
| 6 | No linear OOA(4243, 252, F4, 2, 183) (dual of [(252, 2), 261, 184]-NRT-code) | [i] | ||
| 7 | No linear OOA(4240, 252, F4, 2, 180) (dual of [(252, 2), 264, 181]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4240, 252, F4, 3, 180) (dual of [(252, 3), 516, 181]-NRT-code) | [i] | ||
| 9 | No digital (60, 240, 252)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |