Information on Result #547641
There is no linear OA(2756, 84, F27, 54) (dual of [84, 28, 55]-code), because residual code would yield OA(272, 29, S27, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 755 > 272 [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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No linear OA(2757, 85, F27, 55) (dual of [85, 28, 56]-code) | [i] | Truncation | |
| 2 | No linear OA(2758, 86, F27, 56) (dual of [86, 28, 57]-code) | [i] | ||
| 3 | No linear OA(2759, 87, F27, 57) (dual of [87, 28, 58]-code) | [i] | ||
| 4 | No linear OA(2760, 88, F27, 58) (dual of [88, 28, 59]-code) | [i] | ||
| 5 | No linear OA(2761, 89, F27, 59) (dual of [89, 28, 60]-code) | [i] | ||
| 6 | No linear OA(2762, 90, F27, 60) (dual of [90, 28, 61]-code) | [i] | ||
| 7 | No linear OA(2763, 91, F27, 61) (dual of [91, 28, 62]-code) | [i] | ||
| 8 | No linear OA(2764, 92, F27, 62) (dual of [92, 28, 63]-code) | [i] | ||
| 9 | No linear OA(2765, 93, F27, 63) (dual of [93, 28, 64]-code) | [i] | ||
| 10 | No linear OA(2766, 94, F27, 64) (dual of [94, 28, 65]-code) | [i] | ||
| 11 | No linear OA(2767, 95, F27, 65) (dual of [95, 28, 66]-code) | [i] | ||
| 12 | No linear OA(2768, 96, F27, 66) (dual of [96, 28, 67]-code) | [i] | ||
| 13 | No linear OA(2769, 97, F27, 67) (dual of [97, 28, 68]-code) | [i] | ||
| 14 | No linear OA(2770, 98, F27, 68) (dual of [98, 28, 69]-code) | [i] | ||
| 15 | No linear OA(2771, 99, F27, 69) (dual of [99, 28, 70]-code) | [i] | ||
| 16 | No linear OA(2772, 100, F27, 70) (dual of [100, 28, 71]-code) | [i] | ||
| 17 | No linear OA(2773, 101, F27, 71) (dual of [101, 28, 72]-code) | [i] | ||
| 18 | No linear OOA(2757, 84, F27, 2, 55) (dual of [(84, 2), 111, 56]-NRT-code) | [i] | m-Reduction for OOAs | |
| 19 | No linear OOA(2758, 84, F27, 2, 56) (dual of [(84, 2), 110, 57]-NRT-code) | [i] | ||
| 20 | No linear OOA(2759, 84, F27, 2, 57) (dual of [(84, 2), 109, 58]-NRT-code) | [i] | ||
| 21 | No linear OOA(2760, 84, F27, 2, 58) (dual of [(84, 2), 108, 59]-NRT-code) | [i] | ||
| 22 | No linear OOA(2761, 84, F27, 2, 59) (dual of [(84, 2), 107, 60]-NRT-code) | [i] | ||
| 23 | No linear OOA(2762, 84, F27, 2, 60) (dual of [(84, 2), 106, 61]-NRT-code) | [i] | ||
| 24 | No linear OOA(2763, 84, F27, 2, 61) (dual of [(84, 2), 105, 62]-NRT-code) | [i] | ||
| 25 | No linear OOA(2764, 84, F27, 2, 62) (dual of [(84, 2), 104, 63]-NRT-code) | [i] | ||
| 26 | No linear OOA(2765, 84, F27, 2, 63) (dual of [(84, 2), 103, 64]-NRT-code) | [i] | ||
| 27 | No linear OOA(2766, 84, F27, 2, 64) (dual of [(84, 2), 102, 65]-NRT-code) | [i] | ||
| 28 | No linear OOA(2767, 84, F27, 2, 65) (dual of [(84, 2), 101, 66]-NRT-code) | [i] | ||
| 29 | No linear OOA(2768, 84, F27, 2, 66) (dual of [(84, 2), 100, 67]-NRT-code) | [i] | ||
| 30 | No linear OOA(2769, 84, F27, 2, 67) (dual of [(84, 2), 99, 68]-NRT-code) | [i] | ||
| 31 | No linear OOA(2770, 84, F27, 2, 68) (dual of [(84, 2), 98, 69]-NRT-code) | [i] | ||
| 32 | No linear OOA(2771, 84, F27, 2, 69) (dual of [(84, 2), 97, 70]-NRT-code) | [i] | ||
| 33 | No linear OOA(2772, 84, F27, 2, 70) (dual of [(84, 2), 96, 71]-NRT-code) | [i] | ||
| 34 | No linear OOA(2773, 84, F27, 2, 71) (dual of [(84, 2), 95, 72]-NRT-code) | [i] | ||
| 35 | No linear OOA(2756, 84, F27, 2, 54) (dual of [(84, 2), 112, 55]-NRT-code) | [i] | Depth Reduction | |
| 36 | No digital (2, 56, 84)-net over F27 | [i] | Extracting Embedded Orthogonal Array | |
| 37 | No linear OA(2754, 110, F27, 52) (dual of [110, 56, 53]-code) | [i] | Construction Y1 (Bound) | |