Information on Result #546718
There is no linear OA(3170, 210, F3, 111) (dual of [210, 40, 112]-code), because residual code would yield OA(359, 98, S3, 37), but
- the linear programming bound shows that M ≥ 669 706575 926673 602832 294393 126699 440696 899104 765650 881469 270113 504934 632053 / 45175 106642 610955 544989 816374 596571 195177 978293 > 359 [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(3171, 211, F3, 112) (dual of [211, 40, 113]-code) | [i] | Truncation | |
| 2 | No linear OA(3172, 212, F3, 113) (dual of [212, 40, 114]-code) | [i] | ||
| 3 | No linear OOA(3171, 210, F3, 2, 112) (dual of [(210, 2), 249, 113]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3172, 210, F3, 2, 113) (dual of [(210, 2), 248, 114]-NRT-code) | [i] | ||
| 5 | No linear OOA(3170, 210, F3, 2, 111) (dual of [(210, 2), 250, 112]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3170, 210, F3, 3, 111) (dual of [(210, 3), 460, 112]-NRT-code) | [i] | ||
| 7 | No linear OOA(3170, 210, F3, 4, 111) (dual of [(210, 4), 670, 112]-NRT-code) | [i] | ||
| 8 | No linear OOA(3170, 210, F3, 5, 111) (dual of [(210, 5), 880, 112]-NRT-code) | [i] | ||
| 9 | No digital (59, 170, 210)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |