Information on Result #547497
There is no linear OA(4258, 365, F4, 188) (dual of [365, 107, 189]-code), because residual code would yield OA(470, 176, S4, 47), but
- 1 times truncation [i] would yield OA(469, 175, S4, 46), but
- the linear programming bound shows that M ≥ 672974 508783 713085 919446 392721 434812 374063 221813 152066 788676 290147 045574 983959 198536 005103 820640 027801 847804 723200 000000 / 1 829712 211075 097010 907956 226624 270704 376891 436886 295247 592787 694007 310519 329949 > 469 [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(4259, 366, F4, 189) (dual of [366, 107, 190]-code) | [i] | Truncation | |
| 2 | No linear OA(4260, 367, F4, 190) (dual of [367, 107, 191]-code) | [i] | ||
| 3 | No linear OOA(4259, 365, F4, 2, 189) (dual of [(365, 2), 471, 190]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(4260, 365, F4, 2, 190) (dual of [(365, 2), 470, 191]-NRT-code) | [i] | ||
| 5 | No linear OOA(4258, 365, F4, 2, 188) (dual of [(365, 2), 472, 189]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(4258, 365, F4, 3, 188) (dual of [(365, 3), 837, 189]-NRT-code) | [i] | ||
| 7 | No digital (70, 258, 365)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |