Information on Result #546633
There is no linear OA(3140, 204, F3, 90) (dual of [204, 64, 91]-code), because residual code would yield OA(350, 113, S3, 30), but
- the linear programming bound shows that M ≥ 596 570195 583823 721692 911689 409545 159333 416347 007509 353942 840802 048696 218909 803001 021000 425338 904291 291412 200954 459797 559193 112998 126796 056497 666716 210000 / 790 509540 724661 767547 670804 913087 923304 064947 691066 061183 661201 682713 479390 203130 739891 928552 692939 503065 752658 282066 469332 139629 > 350 [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(3141, 205, F3, 91) (dual of [205, 64, 92]-code) | [i] | Truncation | |
| 2 | No linear OA(3142, 206, F3, 92) (dual of [206, 64, 93]-code) | [i] | ||
| 3 | No linear OOA(3141, 204, F3, 2, 91) (dual of [(204, 2), 267, 92]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3142, 204, F3, 2, 92) (dual of [(204, 2), 266, 93]-NRT-code) | [i] | ||
| 5 | No linear OOA(3140, 204, F3, 2, 90) (dual of [(204, 2), 268, 91]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3140, 204, F3, 3, 90) (dual of [(204, 3), 472, 91]-NRT-code) | [i] | ||
| 7 | No linear OOA(3140, 204, F3, 4, 90) (dual of [(204, 4), 676, 91]-NRT-code) | [i] | ||
| 8 | No linear OOA(3140, 204, F3, 5, 90) (dual of [(204, 5), 880, 91]-NRT-code) | [i] | ||
| 9 | No digital (50, 140, 204)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |