Information on Result #546734
There is no linear OA(3178, 257, F3, 114) (dual of [257, 79, 115]-code), because residual code would yield OA(364, 142, S3, 38), but
- the linear programming bound shows that M ≥ 2846 926043 960650 495051 068515 031396 348457 468672 309930 533525 992494 049197 887626 959665 996392 018123 051568 606408 359969 141109 818434 716934 446451 971089 981651 105587 855809 085244 860263 569249 657907 474743 124647 019708 720445 049205 956233 001230 173765 992166 211584 / 760 430386 438996 947207 913818 687184 087000 934370 497726 262841 427228 927142 510692 279719 900376 732452 532453 744502 189058 083069 971557 640736 908354 474342 397263 004008 984480 127369 741954 835724 634885 413693 063784 405933 734899 188533 > 364 [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(3179, 258, F3, 115) (dual of [258, 79, 116]-code) | [i] | Truncation | |
| 2 | No linear OA(3180, 259, F3, 116) (dual of [259, 79, 117]-code) | [i] | ||
| 3 | No linear OOA(3179, 257, F3, 2, 115) (dual of [(257, 2), 335, 116]-NRT-code) | [i] | m-Reduction for OOAs | |
| 4 | No linear OOA(3180, 257, F3, 2, 116) (dual of [(257, 2), 334, 117]-NRT-code) | [i] | ||
| 5 | No linear OOA(3178, 257, F3, 2, 114) (dual of [(257, 2), 336, 115]-NRT-code) | [i] | Depth Reduction | |
| 6 | No linear OOA(3178, 257, F3, 3, 114) (dual of [(257, 3), 593, 115]-NRT-code) | [i] | ||
| 7 | No linear OOA(3178, 257, F3, 4, 114) (dual of [(257, 4), 850, 115]-NRT-code) | [i] | ||
| 8 | No linear OOA(3178, 257, F3, 5, 114) (dual of [(257, 5), 1107, 115]-NRT-code) | [i] | ||
| 9 | No digital (64, 178, 257)-net over F3 | [i] | Extracting Embedded Orthogonal Array | |