Information on Result #547997
There is no linear OA(8118, 276, F8, 100) (dual of [276, 158, 101]-code), because construction Y1 would yield
- OA(8117, 140, S8, 100), but
- the linear programming bound shows that M ≥ 2 610180 317140 959157 407235 870225 536882 213600 222274 356475 248057 654929 251624 957834 778793 578988 176724 604529 956295 515201 688207 097856 / 534 269890 876318 386075 > 8117 [i]
- linear OA(8158, 276, F8, 136) (dual of [276, 118, 137]-code), but
- discarding factors / shortening the dual code would yield linear OA(8158, 266, F8, 136) (dual of [266, 108, 137]-code), but
- residual code [i] would yield OA(822, 129, S8, 17), but
- 1 times truncation [i] would yield OA(821, 128, S8, 16), but
- the linear programming bound shows that M ≥ 1 008968 613742 170487 095115 575000 563712 / 108734 057573 457133 > 821 [i]
- 1 times truncation [i] would yield OA(821, 128, S8, 16), but
- residual code [i] would yield OA(822, 129, S8, 17), but
- discarding factors / shortening the dual code would yield linear OA(8158, 266, F8, 136) (dual of [266, 108, 137]-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 OOA(8118, 276, F8, 2, 100) (dual of [(276, 2), 434, 101]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(8118, 276, F8, 3, 100) (dual of [(276, 3), 710, 101]-NRT-code) | [i] | ||
| 3 | No digital (18, 118, 276)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |