Information on Result #547993
There is no linear OA(8106, 272, F8, 90) (dual of [272, 166, 91]-code), because construction Y1 would yield
- OA(8105, 128, S8, 90), but
- the linear programming bound shows that M ≥ 21950 796382 814438 782744 864463 381336 127596 030073 856912 690696 782531 039738 810829 256630 497562 292754 935128 215485 677031 129088 / 296811 395949 608374 280875 > 8105 [i]
- linear OA(8166, 272, F8, 144) (dual of [272, 106, 145]-code), but
- discarding factors / shortening the dual code would yield linear OA(8166, 244, F8, 144) (dual of [244, 78, 145]-code), but
- residual code [i] would yield OA(822, 99, S8, 18), but
- the linear programming bound shows that M ≥ 7 461344 900772 163012 506367 600128 688128 / 94986 278747 950549 > 822 [i]
- residual code [i] would yield OA(822, 99, S8, 18), but
- discarding factors / shortening the dual code would yield linear OA(8166, 244, F8, 144) (dual of [244, 78, 145]-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(8106, 272, F8, 2, 90) (dual of [(272, 2), 438, 91]-NRT-code) | [i] | Depth Reduction | |
| 2 | No linear OOA(8106, 272, F8, 3, 90) (dual of [(272, 3), 710, 91]-NRT-code) | [i] | ||
| 3 | No digital (16, 106, 272)-net over F8 | [i] | Extracting Embedded Orthogonal Array | |