Information on Result #548029
There is no linear OA(9127, 261, F9, 110) (dual of [261, 134, 111]-code), because construction Y1 would yield
- OA(9126, 144, S9, 110), but
- the linear programming bound shows that M ≥ 13985 352127 709815 135823 207322 213660 655679 036196 057151 464807 486617 148753 068973 647813 060841 422573 871412 475846 092090 726797 721652 094761 117031 / 7512 322263 802055 > 9126 [i]
- linear OA(9134, 261, F9, 117) (dual of [261, 127, 118]-code), but
- discarding factors / shortening the dual code would yield linear OA(9134, 251, F9, 117) (dual of [251, 117, 118]-code), but
- residual code [i] would yield OA(917, 133, S9, 13), but
- 1 times truncation [i] would yield OA(916, 132, S9, 12), but
- the linear programming bound shows that M ≥ 366759 481988 110308 514537 173543 / 191 274702 307783 > 916 [i]
- 1 times truncation [i] would yield OA(916, 132, S9, 12), but
- residual code [i] would yield OA(917, 133, S9, 13), but
- discarding factors / shortening the dual code would yield linear OA(9134, 251, F9, 117) (dual of [251, 117, 118]-code), 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(9128, 262, F9, 111) (dual of [262, 134, 112]-code) | [i] | Truncation | |
| 2 | No linear OA(9129, 263, F9, 112) (dual of [263, 134, 113]-code) | [i] | ||
| 3 | No linear OA(9130, 264, F9, 113) (dual of [264, 134, 114]-code) | [i] | ||
| 4 | No linear OA(9131, 265, F9, 114) (dual of [265, 134, 115]-code) | [i] | ||
| 5 | No linear OA(9132, 266, F9, 115) (dual of [266, 134, 116]-code) | [i] | ||
| 6 | No linear OA(9133, 267, F9, 116) (dual of [267, 134, 117]-code) | [i] | ||
| 7 | No linear OOA(9128, 261, F9, 2, 111) (dual of [(261, 2), 394, 112]-NRT-code) | [i] | m-Reduction for OOAs | |
| 8 | No linear OOA(9129, 261, F9, 2, 112) (dual of [(261, 2), 393, 113]-NRT-code) | [i] | ||
| 9 | No linear OOA(9130, 261, F9, 2, 113) (dual of [(261, 2), 392, 114]-NRT-code) | [i] | ||
| 10 | No linear OOA(9131, 261, F9, 2, 114) (dual of [(261, 2), 391, 115]-NRT-code) | [i] | ||
| 11 | No linear OOA(9132, 261, F9, 2, 115) (dual of [(261, 2), 390, 116]-NRT-code) | [i] | ||
| 12 | No linear OOA(9133, 261, F9, 2, 116) (dual of [(261, 2), 389, 117]-NRT-code) | [i] | ||
| 13 | No linear OOA(9127, 261, F9, 2, 110) (dual of [(261, 2), 395, 111]-NRT-code) | [i] | Depth Reduction | |
| 14 | No linear OOA(9127, 261, F9, 3, 110) (dual of [(261, 3), 656, 111]-NRT-code) | [i] | ||
| 15 | No digital (17, 127, 261)-net over F9 | [i] | Extracting Embedded Orthogonal Array | |