Information on Result #1849728
There is no (105, m, 116)-net in base 2 for arbitrarily large m, because m-reduction would yield (105, 687, 116)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2687, 116, S2, 6, 582), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 390400 711443 043346 240542 217870 009549 396314 282240 782434 884638 035774 632464 576736 467266 248688 239352 267864 502642 219794 477095 888160 987318 329192 966517 502509 319281 832614 256841 564247 522037 544530 477076 672478 796027 265024 / 583 > 2687 [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 (105, 115)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (105, 105+k, 116)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (105, m, 116)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (105, 105+k, 116)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (105, m, 116)-net over F2 with unbounded m | [i] | ||