Information on Result #547992
There is no linear OA(8100, 257, F8, 85) (dual of [257, 157, 86]-code), because construction Y1 would yield
- OA(899, 121, S8, 85), but
- the linear programming bound shows that M ≥ 16 585536 119637 517746 844303 974375 958556 579597 629933 708370 240352 981117 333510 722093 451763 358747 047640 569273 647104 / 63 671965 472816 494885 > 899 [i]
- linear OA(8157, 257, F8, 136) (dual of [257, 100, 137]-code), but
- discarding factors / shortening the dual code would yield linear OA(8157, 238, F8, 136) (dual of [238, 81, 137]-code), but
- residual code [i] would yield OA(821, 101, S8, 17), but
- 1 times truncation [i] would yield OA(820, 100, S8, 16), but
- the linear programming bound shows that M ≥ 766 916854 670851 025894 998613 688320 / 621 810617 698353 > 820 [i]
- 1 times truncation [i] would yield OA(820, 100, S8, 16), but
- residual code [i] would yield OA(821, 101, S8, 17), but
- discarding factors / shortening the dual code would yield linear OA(8157, 238, F8, 136) (dual of [238, 81, 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(8100, 257, F8, 2, 85) (dual of [(257, 2), 414, 86]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(8100, 257, F8, 3, 85) (dual of [(257, 3), 671, 86]-NRT-code) | [i] | ||
| 3 | No digital (15, 100, 257)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |