Information on Result #548621
There is no linear OA(4182, 201, F4, 136) (dual of [201, 19, 137]-code), because construction Y1 would yield
- linear OA(4181, 191, F4, 136) (dual of [191, 10, 137]-code), but
- residual code [i] would yield linear OA(445, 54, F4, 34) (dual of [54, 9, 35]-code), but
- “Gur†bound on codes from Brouwer’s database [i]
- residual code [i] would yield linear OA(445, 54, F4, 34) (dual of [54, 9, 35]-code), but
- OA(419, 201, S4, 10), but
- discarding factors would yield OA(419, 171, S4, 10), but
- the Rao or (dual) Hamming bound shows that M ≥ 281922 389596 > 419 [i]
- discarding factors would yield OA(419, 171, S4, 10), 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(4183, 202, F4, 137) (dual of [202, 19, 138]-code) | [i] | Truncation | |
| 2 | No linear OA(4184, 203, F4, 138) (dual of [203, 19, 139]-code) | [i] | ||
| 3 | No linear OOA(4183, 201, F4, 2, 137) (dual of [(201, 2), 219, 138]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(4184, 201, F4, 2, 138) (dual of [(201, 2), 218, 139]-NRT-code) | [i] | ||
| 5 | No linear OOA(4182, 201, F4, 2, 136) (dual of [(201, 2), 220, 137]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(4182, 201, F4, 3, 136) (dual of [(201, 3), 421, 137]-NRT-code) | [i] | ||
| 7 | No digital (46, 182, 201)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |