Information on Result #546668
There is no linear OA(3153, 211, F3, 99) (dual of [211, 58, 100]-code), because residual code would yield OA(354, 111, S3, 33), but
- the linear programming bound shows that M ≥ 69 521653 500476 614161 153568 439456 634621 343301 061108 091935 969781 672114 860568 911476 164860 756535 387360 911965 492756 797941 739348 801233 686914 510198 029737 162192 836257 832169 499658 440584 424171 453843 297237 778361 993190 002979 / 1 155137 652131 936103 891023 114978 691396 257144 646390 867107 634474 991714 089289 269885 604212 360556 654992 555516 006816 245080 116966 711030 040640 675877 351563 109531 582514 583401 847586 081113 972591 401217 > 354 [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(3154, 212, F3, 100) (dual of [212, 58, 101]-code) | [i] | Truncation | |
| 2 | No linear OA(3155, 213, F3, 101) (dual of [213, 58, 102]-code) | [i] | ||
| 3 | No linear OOA(3154, 211, F3, 2, 100) (dual of [(211, 2), 268, 101]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3155, 211, F3, 2, 101) (dual of [(211, 2), 267, 102]-NRT-code) | [i] | ||
| 5 | No linear OOA(3153, 211, F3, 2, 99) (dual of [(211, 2), 269, 100]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3153, 211, F3, 3, 99) (dual of [(211, 3), 480, 100]-NRT-code) | [i] | ||
| 7 | No linear OOA(3153, 211, F3, 4, 99) (dual of [(211, 4), 691, 100]-NRT-code) | [i] | ||
| 8 | No linear OOA(3153, 211, F3, 5, 99) (dual of [(211, 5), 902, 100]-NRT-code) | [i] | ||
| 9 | No digital (54, 153, 211)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |