Information on Result #547143
There is no linear OA(4149, 239, F4, 108) (dual of [239, 90, 109]-code), because residual code would yield OA(441, 130, S4, 27), but
- the linear programming bound shows that M ≥ 21 043123 812010 240591 636510 926917 514688 253132 800000 / 4 066822 030762 196031 534869 > 441 [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(4150, 240, F4, 109) (dual of [240, 90, 110]-code) | [i] | Truncation | |
| 2 | No linear OA(4151, 241, F4, 110) (dual of [241, 90, 111]-code) | [i] | ||
| 3 | No linear OA(4152, 242, F4, 111) (dual of [242, 90, 112]-code) | [i] | ||
| 4 | No linear OOA(4150, 239, F4, 2, 109) (dual of [(239, 2), 328, 110]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4151, 239, F4, 2, 110) (dual of [(239, 2), 327, 111]-NRT-code) | [i] | ||
| 6 | No linear OOA(4152, 239, F4, 2, 111) (dual of [(239, 2), 326, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(4149, 239, F4, 2, 108) (dual of [(239, 2), 329, 109]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4149, 239, F4, 3, 108) (dual of [(239, 3), 568, 109]-NRT-code) | [i] | ||
| 9 | No digital (41, 149, 239)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |
| 10 | No linear OA(496, 245, F4, 67) (dual of [245, 149, 68]-code) | [i] | Construction Y1 (Bound) | |