Information on Result #547870
There is no linear OA(4132, 178, F4, 95) (dual of [178, 46, 96]-code), because construction Y1 would yield
- OA(4131, 149, S4, 95), but
- the linear programming bound shows that M ≥ 33368 039747 905148 197531 005626 408113 677562 887057 731053 159021 618938 897974 262171 069449 240576 / 3975 943153 > 4131 [i]
- OA(446, 178, S4, 29), but
- discarding factors would yield OA(446, 174, S4, 29), but
- the linear programming bound shows that M ≥ 8506 289708 537907 430011 501124 929257 400094 961052 942336 000000 / 1 703346 550862 338223 360728 253441 > 446 [i]
- discarding factors would yield OA(446, 174, S4, 29), 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(4133, 179, F4, 96) (dual of [179, 46, 97]-code) | [i] | Truncation | |
| 2 | No linear OOA(4133, 178, F4, 2, 96) (dual of [(178, 2), 223, 97]-NRT-code) | [i] | m-Reduction for OOAs | |
| 3 | No linear OOA(4132, 178, F4, 2, 95) (dual of [(178, 2), 224, 96]-NRT-code) | [i] | Depth Reduction | |
| 4 | No linear OOA(4132, 178, F4, 3, 95) (dual of [(178, 3), 402, 96]-NRT-code) | [i] | ||
| 5 | No digital (37, 132, 178)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |