Information on Result #599186
There is no digital (70, 196, 268)-net over F3, because extracting embedded orthogonal array would yield linear OA(3196, 268, F3, 126) (dual of [268, 72, 127]-code), but
- residual code [i] would yield OA(370, 141, S3, 42), but
- the linear programming bound shows that M ≥ 4277 565698 839384 010170 589716 887095 058169 368020 564397 199414 212109 971383 967143 580539 372570 911510 043347 952663 370579 446414 731408 702577 108148 457502 649267 485100 181078 723724 847585 165364 997228 804035 089921 869721 103476 315522 380830 764656 460391 496415 038990 939869 773410 036939 045606 959626 591763 297984 748711 096468 331745 518174 622445 985981 095385 / 1 551512 830602 858860 338181 158623 054002 886482 377025 245272 895207 545358 537220 058041 448632 273527 418957 014308 934517 283125 135524 500935 334910 128739 898590 747907 120072 589632 997168 116604 990877 528573 097744 651010 819159 741742 497065 834837 245926 336361 938850 088121 503037 789061 126850 003819 367246 912997 850917 454263 > 370 [i]
Mode: Bound (linear).
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | No digital (70, 197, 268)-net over F3 | [i] | m-Reduction | |
| 2 | No digital (70, 198, 268)-net over F3 | [i] | ||