Information on Result #547637
There is no linear OA(2552, 78, F25, 50) (dual of [78, 26, 51]-code), because residual code would yield OA(252, 27, S25, 2), but
- bound for OAs with strength k = 2 [i]
- the Rao or (dual) Hamming bound shows that M ≥ 649 > 252 [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(2553, 79, F25, 51) (dual of [79, 26, 52]-code) | [i] | Truncation | |
| 2 | No linear OA(2554, 80, F25, 52) (dual of [80, 26, 53]-code) | [i] | ||
| 3 | No linear OA(2555, 81, F25, 53) (dual of [81, 26, 54]-code) | [i] | ||
| 4 | No linear OA(2556, 82, F25, 54) (dual of [82, 26, 55]-code) | [i] | ||
| 5 | No linear OA(2557, 83, F25, 55) (dual of [83, 26, 56]-code) | [i] | ||
| 6 | No linear OA(2558, 84, F25, 56) (dual of [84, 26, 57]-code) | [i] | ||
| 7 | No linear OA(2559, 85, F25, 57) (dual of [85, 26, 58]-code) | [i] | ||
| 8 | No linear OA(2560, 86, F25, 58) (dual of [86, 26, 59]-code) | [i] | ||
| 9 | No linear OA(2561, 87, F25, 59) (dual of [87, 26, 60]-code) | [i] | ||
| 10 | No linear OA(2562, 88, F25, 60) (dual of [88, 26, 61]-code) | [i] | ||
| 11 | No linear OA(2563, 89, F25, 61) (dual of [89, 26, 62]-code) | [i] | ||
| 12 | No linear OA(2564, 90, F25, 62) (dual of [90, 26, 63]-code) | [i] | ||
| 13 | No linear OA(2565, 91, F25, 63) (dual of [91, 26, 64]-code) | [i] | ||
| 14 | No linear OA(2566, 92, F25, 64) (dual of [92, 26, 65]-code) | [i] | ||
| 15 | No linear OA(2567, 93, F25, 65) (dual of [93, 26, 66]-code) | [i] | ||
| 16 | No linear OA(2568, 94, F25, 66) (dual of [94, 26, 67]-code) | [i] | ||
| 17 | No linear OOA(2553, 78, F25, 2, 51) (dual of [(78, 2), 103, 52]-NRT-code) | [i] | m-Reduction for OOAs | |
| 18 | No linear OOA(2554, 78, F25, 2, 52) (dual of [(78, 2), 102, 53]-NRT-code) | [i] | ||
| 19 | No linear OOA(2555, 78, F25, 2, 53) (dual of [(78, 2), 101, 54]-NRT-code) | [i] | ||
| 20 | No linear OOA(2556, 78, F25, 2, 54) (dual of [(78, 2), 100, 55]-NRT-code) | [i] | ||
| 21 | No linear OOA(2557, 78, F25, 2, 55) (dual of [(78, 2), 99, 56]-NRT-code) | [i] | ||
| 22 | No linear OOA(2558, 78, F25, 2, 56) (dual of [(78, 2), 98, 57]-NRT-code) | [i] | ||
| 23 | No linear OOA(2559, 78, F25, 2, 57) (dual of [(78, 2), 97, 58]-NRT-code) | [i] | ||
| 24 | No linear OOA(2560, 78, F25, 2, 58) (dual of [(78, 2), 96, 59]-NRT-code) | [i] | ||
| 25 | No linear OOA(2561, 78, F25, 2, 59) (dual of [(78, 2), 95, 60]-NRT-code) | [i] | ||
| 26 | No linear OOA(2562, 78, F25, 2, 60) (dual of [(78, 2), 94, 61]-NRT-code) | [i] | ||
| 27 | No linear OOA(2563, 78, F25, 2, 61) (dual of [(78, 2), 93, 62]-NRT-code) | [i] | ||
| 28 | No linear OOA(2564, 78, F25, 2, 62) (dual of [(78, 2), 92, 63]-NRT-code) | [i] | ||
| 29 | No linear OOA(2565, 78, F25, 2, 63) (dual of [(78, 2), 91, 64]-NRT-code) | [i] | ||
| 30 | No linear OOA(2566, 78, F25, 2, 64) (dual of [(78, 2), 90, 65]-NRT-code) | [i] | ||
| 31 | No linear OOA(2567, 78, F25, 2, 65) (dual of [(78, 2), 89, 66]-NRT-code) | [i] | ||
| 32 | No linear OOA(2568, 78, F25, 2, 66) (dual of [(78, 2), 88, 67]-NRT-code) | [i] | ||
| 33 | No linear OOA(2552, 78, F25, 2, 50) (dual of [(78, 2), 104, 51]-NRT-code) | [i] | Depth Reduction | |
| 34 | No digital (2, 52, 78)-net over F25 | [i] | Extracting Embedded Orthogonal Array | |
| 35 | No linear OA(2550, 102, F25, 48) (dual of [102, 52, 49]-code) | [i] | Construction Y1 (Bound) | |