Information on Result #547430
There is no linear OA(4240, 317, F4, 176) (dual of [317, 77, 177]-code), because residual code would yield OA(464, 140, S4, 44), but
- the linear programming bound shows that M ≥ 6 055971 130979 717035 237533 763765 896035 104411 078322 823391 498324 273826 156962 484218 588303 215205 346683 113225 234756 746893 442044 988412 906254 866058 803915 928912 265216 000000 / 17465 630993 245964 374557 288355 588936 264526 909741 890553 067641 295523 141418 950639 065672 191422 532782 852686 274622 640710 777054 531879 > 464 [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(4241, 318, F4, 177) (dual of [318, 77, 178]-code) | [i] | Truncation | |
| 2 | No linear OA(4242, 319, F4, 178) (dual of [319, 77, 179]-code) | [i] | ||
| 3 | No linear OA(4243, 320, F4, 179) (dual of [320, 77, 180]-code) | [i] | ||
| 4 | No linear OOA(4241, 317, F4, 2, 177) (dual of [(317, 2), 393, 178]-NRT-code) | [i] | m-Reduction for OOAs | |
| 5 | No linear OOA(4242, 317, F4, 2, 178) (dual of [(317, 2), 392, 179]-NRT-code) | [i] | ||
| 6 | No linear OOA(4243, 317, F4, 2, 179) (dual of [(317, 2), 391, 180]-NRT-code) | [i] | ||
| 7 | No linear OOA(4240, 317, F4, 2, 176) (dual of [(317, 2), 394, 177]-NRT-code) | [i] | Depth Reduction | |
| 8 | No linear OOA(4240, 317, F4, 3, 176) (dual of [(317, 3), 711, 177]-NRT-code) | [i] | ||
| 9 | No digital (64, 240, 317)-net over F4 | [i] | Extracting Embedded Orthogonal Array | |