Information on Result #547779
There is no linear OA(3132, 202, F3, 84) (dual of [202, 70, 85]-code), because construction Y1 would yield
- linear OA(3131, 163, F3, 84) (dual of [163, 32, 85]-code), but
- construction Y1 [i] would yield
- OA(3130, 147, S3, 84), but
- the linear programming bound shows that M ≥ 610951 874237 245179 799757 396293 504258 972145 948730 720728 290459 967541 402306 / 4917 657235 > 3130 [i]
- OA(332, 163, S3, 16), but
- discarding factors would yield OA(332, 156, S3, 16), but
- the Rao or (dual) Hamming bound shows that M ≥ 1906 607562 901809 > 332 [i]
- discarding factors would yield OA(332, 156, S3, 16), but
- OA(3130, 147, S3, 84), but
- construction Y1 [i] would yield
- OA(370, 202, S3, 39), but
- discarding factors would yield OA(370, 201, S3, 39), but
- the linear programming bound shows that M ≥ 113 349189 137258 716153 960396 901943 653307 523624 962713 490500 568615 819372 696809 220000 000000 / 44072 627437 445072 457879 396444 067387 747385 068139 742293 > 370 [i]
- discarding factors would yield OA(370, 201, S3, 39), 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 OOA(3132, 202, F3, 2, 84) (dual of [(202, 2), 272, 85]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(3132, 202, F3, 3, 84) (dual of [(202, 3), 474, 85]-NRT-code) | [i] | ||
| 3 | No linear OOA(3132, 202, F3, 4, 84) (dual of [(202, 4), 676, 85]-NRT-code) | [i] | ||
| 4 | No linear OOA(3132, 202, F3, 5, 84) (dual of [(202, 5), 878, 85]-NRT-code) | [i] | ||
| 5 | No digital (48, 132, 202)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |