Information on Result #547908
There is no linear OA(4200, 230, F4, 149) (dual of [230, 30, 150]-code), because construction Y1 would yield
- linear OA(4199, 214, F4, 149) (dual of [214, 15, 150]-code), but
- 1 times truncation [i] would yield linear OA(4198, 213, F4, 148) (dual of [213, 15, 149]-code), but
- construction Y1 [i] would yield
- linear OA(4197, 205, F4, 148) (dual of [205, 8, 149]-code), but
- construction Y1 [i] would yield
- linear OA(4196, 201, F4, 148) (dual of [201, 5, 149]-code), but
- residual code [i] would yield linear OA(448, 52, F4, 37) (dual of [52, 4, 38]-code), but
- 1 times truncation [i] would yield linear OA(447, 51, F4, 36) (dual of [51, 4, 37]-code), but
- residual code [i] would yield linear OA(448, 52, F4, 37) (dual of [52, 4, 38]-code), but
- OA(48, 205, S4, 4), but
- discarding factors would yield OA(48, 121, S4, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 65704 > 48 [i]
- discarding factors would yield OA(48, 121, S4, 4), but
- linear OA(4196, 201, F4, 148) (dual of [201, 5, 149]-code), but
- construction Y1 [i] would yield
- OA(415, 213, S4, 8), but
- discarding factors would yield OA(415, 135, S4, 8), but
- the Rao or (dual) Hamming bound shows that M ≥ 1082 768311 > 415 [i]
- discarding factors would yield OA(415, 135, S4, 8), but
- linear OA(4197, 205, F4, 148) (dual of [205, 8, 149]-code), but
- construction Y1 [i] would yield
- 1 times truncation [i] would yield linear OA(4198, 213, F4, 148) (dual of [213, 15, 149]-code), but
- OA(430, 230, S4, 16), but
- the linear programming bound shows that M ≥ 57 643098 217881 685156 997061 672960 / 49 293754 184261 > 430 [i]
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(4201, 231, F4, 150) (dual of [231, 30, 151]-code) | [i] | Truncation | |
| 2 | No linear OA(4202, 232, F4, 151) (dual of [232, 30, 152]-code) | [i] | ||
| 3 | No linear OOA(4201, 230, F4, 2, 150) (dual of [(230, 2), 259, 151]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(4202, 230, F4, 2, 151) (dual of [(230, 2), 258, 152]-NRT-code) | [i] | ||
| 5 | No linear OOA(4200, 230, F4, 2, 149) (dual of [(230, 2), 260, 150]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(4200, 230, F4, 3, 149) (dual of [(230, 3), 490, 150]-NRT-code) | [i] | ||
| 7 | No digital (51, 200, 230)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |