Information on Result #547923
There is no linear OA(4256, 265, F4, 192) (dual of [265, 9, 193]-code), because construction Y1 would yield
- linear OA(4255, 261, F4, 192) (dual of [261, 6, 193]-code), but
- construction Y1 [i] would yield
- linear OA(4254, 258, F4, 192) (dual of [258, 4, 193]-code), but
- linear OA(46, 261, F4, 3) (dual of [261, 255, 4]-code or 261-cap in PG(5,4)), but
- construction Y1 [i] would yield
- OA(49, 265, S4, 4), but
- discarding factors would yield OA(49, 242, S4, 4), but
- the Rao or (dual) Hamming bound shows that M ≥ 263176 > 49 [i]
- discarding factors would yield OA(49, 242, S4, 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(4257, 266, F4, 193) (dual of [266, 9, 194]-code) | [i] | Truncation | |
| 2 | No linear OA(4258, 267, F4, 194) (dual of [267, 9, 195]-code) | [i] | ||
| 3 | No linear OA(4259, 268, F4, 195) (dual of [268, 9, 196]-code) | [i] | ||
| 4 | No linear OOA(4257, 265, F4, 2, 193) (dual of [(265, 2), 273, 194]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4258, 265, F4, 2, 194) (dual of [(265, 2), 272, 195]-NRT-code) | [i] | ||
| 6 | No linear OOA(4259, 265, F4, 2, 195) (dual of [(265, 2), 271, 196]-NRT-code) | [i] | ||
| 7 | No linear OOA(4260, 265, F4, 2, 196) (dual of [(265, 2), 270, 197]-NRT-code) | [i] | ||
| 8 | No linear OOA(4256, 265, F4, 2, 192) (dual of [(265, 2), 274, 193]-NRT-code) | [i] | Depth Reduction | |
| 9 | No linear OOA(4256, 265, F4, 3, 192) (dual of [(265, 3), 539, 193]-NRT-code) | [i] | ||
| 10 | No digital (64, 256, 265)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |