Information on Result #546757
There is no linear OA(3185, 237, F3, 120) (dual of [237, 52, 121]-code), because residual code would yield OA(365, 116, S3, 40), but
- the linear programming bound shows that M ≥ 1010 233715 716651 107612 542215 638091 218609 672761 165524 903593 924473 005111 306769 562821 186134 762126 385755 152296 422613 586112 342241 377727 269019 414533 549609 685737 803087 / 94 423144 003278 216048 118473 500831 454684 060079 864523 188758 682434 278034 186489 210172 080884 936271 279930 533580 650501 446289 752944 864745 > 365 [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(3186, 238, F3, 121) (dual of [238, 52, 122]-code) | [i] | Truncation | |
| 2 | No linear OA(3187, 239, F3, 122) (dual of [239, 52, 123]-code) | [i] | ||
| 3 | No linear OOA(3186, 237, F3, 2, 121) (dual of [(237, 2), 288, 122]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3187, 237, F3, 2, 122) (dual of [(237, 2), 287, 123]-NRT-code) | [i] | ||
| 5 | No linear OOA(3185, 237, F3, 2, 120) (dual of [(237, 2), 289, 121]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3185, 237, F3, 3, 120) (dual of [(237, 3), 526, 121]-NRT-code) | [i] | ||
| 7 | No linear OOA(3185, 237, F3, 4, 120) (dual of [(237, 4), 763, 121]-NRT-code) | [i] | ||
| 8 | No linear OOA(3185, 237, F3, 5, 120) (dual of [(237, 5), 1000, 121]-NRT-code) | [i] | ||
| 9 | No digital (65, 185, 237)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |