Information on Result #546669
There is no linear OA(3154, 223, F3, 99) (dual of [223, 69, 100]-code), because residual code would yield OA(355, 123, S3, 33), but
- the linear programming bound shows that M ≥ 148 070708 119494 381097 768298 762064 420941 614688 018061 442730 314757 617739 382441 097813 300293 193176 549890 233732 442129 700432 638201 644702 914535 355721 641913 236632 545448 107728 196475 461463 715767 220573 162925 / 812684 026412 505193 891098 210421 866334 373415 292609 947732 124728 804133 321909 393097 168706 926460 978407 999004 611093 804726 375841 495072 336504 276946 318881 556551 454271 872053 611339 > 355 [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(3155, 224, F3, 100) (dual of [224, 69, 101]-code) | [i] | Truncation | |
| 2 | No linear OA(3156, 225, F3, 101) (dual of [225, 69, 102]-code) | [i] | ||
| 3 | No linear OOA(3155, 223, F3, 2, 100) (dual of [(223, 2), 291, 101]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3156, 223, F3, 2, 101) (dual of [(223, 2), 290, 102]-NRT-code) | [i] | ||
| 5 | No linear OOA(3154, 223, F3, 2, 99) (dual of [(223, 2), 292, 100]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3154, 223, F3, 3, 99) (dual of [(223, 3), 515, 100]-NRT-code) | [i] | ||
| 7 | No linear OOA(3154, 223, F3, 4, 99) (dual of [(223, 4), 738, 100]-NRT-code) | [i] | ||
| 8 | No linear OOA(3154, 223, F3, 5, 99) (dual of [(223, 5), 961, 100]-NRT-code) | [i] | ||
| 9 | No digital (55, 154, 223)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |