Information on Result #548038
There is no linear OA(1678, 124, F16, 73) (dual of [124, 46, 74]-code), because construction Y1 would yield
- OA(1677, 81, S16, 73), but
- the linear programming bound shows that M ≥ 20 058253 259194 796242 490750 709498 450326 191022 155255 442417 783937 598455 532112 408827 665059 378347 638784 / 37999 > 1677 [i]
- linear OA(1646, 124, F16, 43) (dual of [124, 78, 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(1679, 125, F16, 74) (dual of [125, 46, 75]-code) | [i] | Truncation | |
| 2 | No linear OA(1680, 126, F16, 75) (dual of [126, 46, 76]-code) | [i] | ||
| 3 | No linear OA(1681, 127, F16, 76) (dual of [127, 46, 77]-code) | [i] | ||
| 4 | No linear OOA(1679, 124, F16, 2, 74) (dual of [(124, 2), 169, 75]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(1680, 124, F16, 2, 75) (dual of [(124, 2), 168, 76]-NRT-code) | [i] | ||
| 6 | No linear OOA(1681, 124, F16, 2, 76) (dual of [(124, 2), 167, 77]-NRT-code) | [i] | ||
| 7 | No linear OOA(1682, 124, F16, 2, 77) (dual of [(124, 2), 166, 78]-NRT-code) | [i] | ||
| 8 | No linear OOA(1678, 124, F16, 2, 73) (dual of [(124, 2), 170, 74]-NRT-code) | [i] | Depth Reduction | |
| 9 | No digital (5, 78, 124)-net over F16 | [i] | Extracting Embedded Orthogonal Array | |