Information on Result #547965
There is no linear OA(5139, 164, F5, 109) (dual of [164, 25, 110]-code), because construction Y1 would yield
- OA(5138, 148, S5, 109), but
- the linear programming bound shows that M ≥ 86 158555 819318 512642 331328 682663 835348 540649 443889 196923 328992 021307 026760 723601 910285 651683 807373 046875 / 29 425011 > 5138 [i]
- OA(525, 164, S5, 16), but
- discarding factors would yield OA(525, 148, S5, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 313081 833470 800945 > 525 [i]
- discarding factors would yield OA(525, 148, S5, 16), 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(5140, 165, F5, 110) (dual of [165, 25, 111]-code) | [i] | Truncation | |
| 2 | No linear OA(5141, 166, F5, 111) (dual of [166, 25, 112]-code) | [i] | ||
| 3 | No linear OA(5142, 167, F5, 112) (dual of [167, 25, 113]-code) | [i] | ||
| 4 | No linear OA(5143, 168, F5, 113) (dual of [168, 25, 114]-code) | [i] | ||
| 5 | No linear OA(5144, 169, F5, 114) (dual of [169, 25, 115]-code) | [i] | ||
| 6 | No linear OA(5145, 170, F5, 115) (dual of [170, 25, 116]-code) | [i] | ||
| 7 | No linear OA(5146, 171, F5, 116) (dual of [171, 25, 117]-code) | [i] | ||
| 8 | No linear OOA(5140, 164, F5, 2, 110) (dual of [(164, 2), 188, 111]-NRT-code) | [i] | m-Reduction for OOAs | |
| 9 | No linear OOA(5141, 164, F5, 2, 111) (dual of [(164, 2), 187, 112]-NRT-code) | [i] | ||
| 10 | No linear OOA(5142, 164, F5, 2, 112) (dual of [(164, 2), 186, 113]-NRT-code) | [i] | ||
| 11 | No linear OOA(5143, 164, F5, 2, 113) (dual of [(164, 2), 185, 114]-NRT-code) | [i] | ||
| 12 | No linear OOA(5144, 164, F5, 2, 114) (dual of [(164, 2), 184, 115]-NRT-code) | [i] | ||
| 13 | No linear OOA(5145, 164, F5, 2, 115) (dual of [(164, 2), 183, 116]-NRT-code) | [i] | ||
| 14 | No linear OOA(5146, 164, F5, 2, 116) (dual of [(164, 2), 182, 117]-NRT-code) | [i] | ||
| 15 | No linear OOA(5147, 164, F5, 2, 117) (dual of [(164, 2), 181, 118]-NRT-code) | [i] | ||
| 16 | No linear OOA(5148, 164, F5, 2, 118) (dual of [(164, 2), 180, 119]-NRT-code) | [i] | ||
| 17 | No linear OOA(5149, 164, F5, 2, 119) (dual of [(164, 2), 179, 120]-NRT-code) | [i] | ||
| 18 | No linear OOA(5139, 164, F5, 2, 109) (dual of [(164, 2), 189, 110]-NRT-code) | [i] | Depth Reduction | |
| 19 | No linear OOA(5139, 164, F5, 3, 109) (dual of [(164, 3), 353, 110]-NRT-code) | [i] | ||
| 20 | No digital (30, 139, 164)-net over F5 | [i] | Extracting Embedded Orthogonal Array | |
| 21 | No linear OA(5140, 239, F5, 109) (dual of [239, 99, 110]-code) | [i] | Construction Y1 (Bound) | |