Information on Result #548620
There is no linear OA(4166, 188, F4, 124) (dual of [188, 22, 125]-code), because construction Y1 would yield
- linear OA(4165, 176, F4, 124) (dual of [176, 11, 125]-code), but
- residual code [i] would yield linear OA(441, 51, F4, 31) (dual of [51, 10, 32]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(441, 51, F4, 31) (dual of [51, 10, 32]-code), but
- OA(422, 188, S4, 12), but
- discarding factors would yield OA(422, 164, S4, 12), but
- the Rao or (dual) Hamming bound shows that M ≥ 18 187369 733464 > 422 [i]
- discarding factors would yield OA(422, 164, 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(4167, 189, F4, 125) (dual of [189, 22, 126]-code) | [i] | Truncation | |
| 2 | No linear OA(4168, 190, F4, 126) (dual of [190, 22, 127]-code) | [i] | ||
| 3 | No linear OA(4169, 191, F4, 127) (dual of [191, 22, 128]-code) | [i] | ||
| 4 | No linear OOA(4167, 188, F4, 2, 125) (dual of [(188, 2), 209, 126]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4168, 188, F4, 2, 126) (dual of [(188, 2), 208, 127]-NRT-code) | [i] | ||
| 6 | No linear OOA(4169, 188, F4, 2, 127) (dual of [(188, 2), 207, 128]-NRT-code) | [i] | ||
| 7 | No linear OOA(4166, 188, F4, 2, 124) (dual of [(188, 2), 210, 125]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4166, 188, F4, 3, 124) (dual of [(188, 3), 398, 125]-NRT-code) | [i] | ||
| 9 | No digital (42, 166, 188)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |