Information on Result #547633
There is no linear OA(1651, 68, F16, 48) (dual of [68, 17, 49]-code), because residual code would yield OA(163, 19, S16, 3), but
- 1 times truncation [i] would yield OA(162, 18, S16, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 271 > 162 [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(1652, 69, F16, 49) (dual of [69, 17, 50]-code) | [i] | Truncation | |
| 2 | No linear OA(1653, 70, F16, 50) (dual of [70, 17, 51]-code) | [i] | ||
| 3 | No linear OA(1654, 71, F16, 51) (dual of [71, 17, 52]-code) | [i] | ||
| 4 | No linear OA(1655, 72, F16, 52) (dual of [72, 17, 53]-code) | [i] | ||
| 5 | No linear OA(1656, 73, F16, 53) (dual of [73, 17, 54]-code) | [i] | ||
| 6 | No linear OA(1657, 74, F16, 54) (dual of [74, 17, 55]-code) | [i] | ||
| 7 | No linear OA(1658, 75, F16, 55) (dual of [75, 17, 56]-code) | [i] | ||
| 8 | No linear OA(1659, 76, F16, 56) (dual of [76, 17, 57]-code) | [i] | ||
| 9 | No linear OA(1660, 77, F16, 57) (dual of [77, 17, 58]-code) | [i] | ||
| 10 | No linear OOA(1652, 68, F16, 2, 49) (dual of [(68, 2), 84, 50]-NRT-code) | [i] | m-Reduction for OOAs | |
| 11 | No linear OOA(1653, 68, F16, 2, 50) (dual of [(68, 2), 83, 51]-NRT-code) | [i] | ||
| 12 | No linear OOA(1654, 68, F16, 2, 51) (dual of [(68, 2), 82, 52]-NRT-code) | [i] | ||
| 13 | No linear OOA(1655, 68, F16, 2, 52) (dual of [(68, 2), 81, 53]-NRT-code) | [i] | ||
| 14 | No linear OOA(1656, 68, F16, 2, 53) (dual of [(68, 2), 80, 54]-NRT-code) | [i] | ||
| 15 | No linear OOA(1657, 68, F16, 2, 54) (dual of [(68, 2), 79, 55]-NRT-code) | [i] | ||
| 16 | No linear OOA(1658, 68, F16, 2, 55) (dual of [(68, 2), 78, 56]-NRT-code) | [i] | ||
| 17 | No linear OOA(1659, 68, F16, 2, 56) (dual of [(68, 2), 77, 57]-NRT-code) | [i] | ||
| 18 | No linear OOA(1660, 68, F16, 2, 57) (dual of [(68, 2), 76, 58]-NRT-code) | [i] | ||
| 19 | No linear OOA(1651, 68, F16, 2, 48) (dual of [(68, 2), 85, 49]-NRT-code) | [i] | Depth Reduction | |
| 20 | No digital (3, 51, 68)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |
| 21 | No linear OA(1646, 97, F16, 43) (dual of [97, 51, 44]-code) | [i] | Construction Y1 (Bound) | |