Information on Result #548035
There is no linear OA(1662, 108, F16, 58) (dual of [108, 46, 59]-code), because construction Y1 would yield
- OA(1661, 65, S16, 58), but
- the linear programming bound shows that M ≥ 159214 122701 309768 707410 104386 945873 298246 228915 255775 554254 178010 880553 254912 / 5487 > 1661 [i]
- linear OA(1646, 108, F16, 43) (dual of [108, 62, 44]-code), but
- discarding factors / shortening the dual code would yield linear OA(1646, 97, F16, 43) (dual of [97, 51, 44]-code), but
- construction Y1 [i] would yield
- OA(1645, 49, S16, 43), but
- the linear programming bound shows that M ≥ 79 689768 125026 220634 634045 411816 077548 174434 353547 313152 / 47 > 1645 [i]
- linear OA(1651, 97, F16, 48) (dual of [97, 46, 49]-code), but
- discarding factors / shortening the dual code would yield linear OA(1651, 68, F16, 48) (dual of [68, 17, 49]-code), but
- residual code [i] 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]
- 1 times truncation [i] would yield OA(162, 18, S16, 2), but
- residual code [i] would yield OA(163, 19, S16, 3), but
- discarding factors / shortening the dual code would yield linear OA(1651, 68, F16, 48) (dual of [68, 17, 49]-code), but
- OA(1645, 49, S16, 43), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(1646, 97, F16, 43) (dual of [97, 51, 44]-code), but
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(1663, 109, F16, 59) (dual of [109, 46, 60]-code) | [i] | Truncation | |
| 2 | No linear OA(1664, 110, F16, 60) (dual of [110, 46, 61]-code) | [i] | ||
| 3 | No linear OA(1665, 111, F16, 61) (dual of [111, 46, 62]-code) | [i] | ||
| 4 | No linear OA(1666, 112, F16, 62) (dual of [112, 46, 63]-code) | [i] | ||
| 5 | No linear OA(1667, 113, F16, 63) (dual of [113, 46, 64]-code) | [i] | ||
| 6 | No linear OOA(1663, 108, F16, 2, 59) (dual of [(108, 2), 153, 60]-NRT-code) | [i] | m-Reduction for OOAs | |
| 7 | No linear OOA(1664, 108, F16, 2, 60) (dual of [(108, 2), 152, 61]-NRT-code) | [i] | ||
| 8 | No linear OOA(1665, 108, F16, 2, 61) (dual of [(108, 2), 151, 62]-NRT-code) | [i] | ||
| 9 | No linear OOA(1666, 108, F16, 2, 62) (dual of [(108, 2), 150, 63]-NRT-code) | [i] | ||
| 10 | No linear OOA(1667, 108, F16, 2, 63) (dual of [(108, 2), 149, 64]-NRT-code) | [i] | ||
| 11 | No linear OOA(1662, 108, F16, 2, 58) (dual of [(108, 2), 154, 59]-NRT-code) | [i] | Depth Reduction | |
| 12 | No digital (4, 62, 108)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |