Information on Result #1850706
There is no (197, m, 409)-net in base 3 for arbitrarily large m, because m-reduction would yield (197, 2447, 409)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32447, 409, S3, 6, 2250), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8 744466 427356 927176 379485 625944 910414 990972 477489 916006 908980 507537 641970 806639 590942 287264 435971 414347 162145 129051 960071 850643 545329 320234 366786 991007 198746 135891 998717 154353 328197 063807 977517 170685 258791 511650 954791 545852 897929 562740 237420 526142 140206 502944 604085 781741 314184 268015 997289 222950 097250 482952 596929 217036 284226 758384 160681 360867 134437 819802 579229 687129 407506 139302 350577 830426 855156 925119 282813 666027 773086 165789 666619 858488 280739 319261 695293 426780 895421 921094 264113 201144 167030 279420 872311 732537 644547 587172 829071 117863 577692 579711 320855 445027 149841 245188 501393 126318 376765 319612 870019 798826 028376 211094 784488 727700 946777 488231 130096 009522 690515 866308 081359 305382 482023 157128 013323 230005 378802 037501 444518 693588 414377 935642 931808 409414 895614 152848 259314 227949 155274 847255 490313 390494 152944 023381 318496 487331 207074 424104 732178 751904 671477 248319 240624 868093 744810 106441 174635 029882 545910 803231 982607 284254 354720 370325 543553 124361 361247 632172 454336 180646 343471 957124 782863 483289 593862 806483 253553 876268 138580 795638 318386 519781 280938 289887 615522 518098 854853 307653 822817 868930 239786 395437 316367 424004 620301 996853 760329 143264 675854 248597 999741 028373 888371 039929 / 2251 > 32447 [i]
Mode: Bound.
Optimality
Show details for fixed 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 (197, 408)-sequence in base 3 | [i] | Net from Sequence | |
| 2 | No (197, 197+k, 409)-net in base 3 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (197, m, 409)-net in base 3 with unbounded m | [i] | ||
| 4 | No digital (197, 197+k, 409)-net over F3 for arbitrarily large k | [i] | ||
| 5 | No digital (197, m, 409)-net over F3 with unbounded m | [i] | ||