Information on Result #547819
There is no linear OA(3243, 253, F3, 162) (dual of [253, 10, 163]-code), because construction Y1 would yield
- linear OA(3242, 249, F3, 162) (dual of [249, 7, 163]-code), but
- residual code [i] would yield linear OA(380, 86, F3, 54) (dual of [86, 6, 55]-code), but
- residual code [i] would yield linear OA(326, 31, F3, 18) (dual of [31, 5, 19]-code), but
- residual code [i] would yield linear OA(38, 12, F3, 6) (dual of [12, 4, 7]-code), but
- residual code [i] would yield linear OA(326, 31, F3, 18) (dual of [31, 5, 19]-code), but
- residual code [i] would yield linear OA(380, 86, F3, 54) (dual of [86, 6, 55]-code), but
- OA(310, 253, S3, 4), but
- discarding factors would yield OA(310, 172, S3, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 59169 > 310 [i]
- discarding factors would yield OA(310, 172, S3, 4), 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(3244, 254, F3, 163) (dual of [254, 10, 164]-code) | [i] | Truncation | |
| 2 | No linear OA(3245, 255, F3, 164) (dual of [255, 10, 165]-code) | [i] | ||
| 3 | No linear OOA(3244, 253, F3, 2, 163) (dual of [(253, 2), 262, 164]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3245, 253, F3, 2, 164) (dual of [(253, 2), 261, 165]-NRT-code) | [i] | ||
| 5 | No linear OOA(3247, 253, F3, 2, 166) (dual of [(253, 2), 259, 167]-NRT-code) | [i] | ||
| 6 | No linear OOA(3248, 253, F3, 2, 167) (dual of [(253, 2), 258, 168]-NRT-code) | [i] | ||
| 7 | No linear OOA(3249, 253, F3, 2, 168) (dual of [(253, 2), 257, 169]-NRT-code) | [i] | ||
| 8 | No linear OOA(3250, 253, F3, 2, 169) (dual of [(253, 2), 256, 170]-NRT-code) | [i] | ||
| 9 | No linear OOA(3243, 253, F3, 2, 162) (dual of [(253, 2), 263, 163]-NRT-code) | [i] | Depth Reduction | |
| 10 | No linear OOA(3243, 253, F3, 3, 162) (dual of [(253, 3), 516, 163]-NRT-code) | [i] | ||
| 11 | No linear OOA(3243, 253, F3, 4, 162) (dual of [(253, 4), 769, 163]-NRT-code) | [i] | ||
| 12 | No linear OOA(3243, 253, F3, 5, 162) (dual of [(253, 5), 1022, 163]-NRT-code) | [i] | ||
| 13 | No digital (81, 243, 253)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |
| 14 | No linear OA(3244, 259, F3, 162) (dual of [259, 15, 163]-code) | [i] | Construction Y1 (Bound) | |