Information on Result #548623
There is no linear OA(4215, 238, F4, 160) (dual of [238, 23, 161]-code), because construction Y1 would yield
- linear OA(4214, 226, F4, 160) (dual of [226, 12, 161]-code), but
- construction Y1 [i] would yield
- linear OA(4213, 220, F4, 160) (dual of [220, 7, 161]-code), but
- residual code [i] would yield linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- residual code [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]
- residual code [i] would yield linear OA(413, 18, F4, 10) (dual of [18, 5, 11]-code), but
- residual code [i] would yield linear OA(453, 59, F4, 40) (dual of [59, 6, 41]-code), but
- OA(412, 226, 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
- linear OA(4213, 220, F4, 160) (dual of [220, 7, 161]-code), but
- construction Y1 [i] would yield
- OA(423, 238, S4, 12), but
- discarding factors would yield OA(423, 205, S4, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 70 503355 038244 > 423 [i]
- discarding factors would yield OA(423, 205, S4, 12), 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(4216, 239, F4, 161) (dual of [239, 23, 162]-code) | [i] | Truncation | |
| 2 | No linear OA(4217, 240, F4, 162) (dual of [240, 23, 163]-code) | [i] | ||
| 3 | No linear OA(4218, 241, F4, 163) (dual of [241, 23, 164]-code) | [i] | ||
| 4 | No linear OOA(4216, 238, F4, 2, 161) (dual of [(238, 2), 260, 162]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4217, 238, F4, 2, 162) (dual of [(238, 2), 259, 163]-NRT-code) | [i] | ||
| 6 | No linear OOA(4218, 238, F4, 2, 163) (dual of [(238, 2), 258, 164]-NRT-code) | [i] | ||
| 7 | No linear OOA(4215, 238, F4, 2, 160) (dual of [(238, 2), 261, 161]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4215, 238, F4, 3, 160) (dual of [(238, 3), 499, 161]-NRT-code) | [i] | ||
| 9 | No digital (55, 215, 238)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |