Information on Result #548693
There is no linear OA(828, 76, F8, 24) (dual of [76, 48, 25]-code), because construction Y1 would yield
- linear OA(827, 34, F8, 24) (dual of [34, 7, 25]-code), but
- construction Y1 [i] would yield
- OA(826, 28, S8, 24), but
- the (dual) Plotkin bound shows that M ≥ 9 671406 556917 033397 649408 / 25 > 826 [i]
- OA(87, 34, S8, 6), but
- discarding factors would yield OA(87, 32, S8, 6), but
- the linear programming bound shows that M ≥ 3784 900608 / 1729 > 87 [i]
- discarding factors would yield OA(87, 32, S8, 6), but
- OA(826, 28, S8, 24), but
- construction Y1 [i] would yield
- linear OA(848, 76, F8, 42) (dual of [76, 28, 43]-code), but
- discarding factors / shortening the dual code would yield linear OA(848, 58, F8, 42) (dual of [58, 10, 43]-code), but
- construction Y1 [i] would yield
- linear OA(847, 50, F8, 42) (dual of [50, 3, 43]-code), but
- “Hi4†bound on codes from Brouwer’s database [i]
- OA(810, 58, S8, 8), but
- discarding factors would yield OA(810, 57, S8, 8), but
- the linear programming bound shows that M ≥ 1426 626655 027200 / 1 315507 > 810 [i]
- discarding factors would yield OA(810, 57, S8, 8), but
- linear OA(847, 50, F8, 42) (dual of [50, 3, 43]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(848, 58, F8, 42) (dual of [58, 10, 43]-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.
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(829, 77, F8, 25) (dual of [77, 48, 26]-code) | [i] | Truncation | |
| 2 | No linear OA(830, 78, F8, 26) (dual of [78, 48, 27]-code) | [i] | ||
| 3 | No linear OOA(829, 76, F8, 2, 25) (dual of [(76, 2), 123, 26]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(830, 76, F8, 2, 26) (dual of [(76, 2), 122, 27]-NRT-code) | [i] | ||
| 5 | No linear OOA(828, 76, F8, 2, 24) (dual of [(76, 2), 124, 25]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(828, 76, F8, 3, 24) (dual of [(76, 3), 200, 25]-NRT-code) | [i] | ||
| 7 | No digital (4, 28, 76)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |