Information on Result #1851615
There is no (25, m, 115)-net in base 5 for arbitrarily large m, because m-reduction would yield (25, 341, 115)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(5341, 115, S5, 3, 316), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7 255291 057944 128305 080657 289047 574449 645913 053074 405564 353826 153300 402474 017381 124892 980607 510857 610077 822122 360284 358895 931170 756685 031135 077416 901528 582102 320157 336859 916207 573206 013739 441572 340410 115116 160483 239582 390524 446964 263916 015625 / 317 > 5341 [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 (25, 114)-sequence in base 5 | [i] | Net from Sequence | |
| 2 | No (25, 25+k, 115)-net in base 5 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (25, m, 115)-net in base 5 with unbounded m | [i] | ||
| 4 | No digital (25, 25+k, 115)-net over F5 for arbitrarily large k | [i] | ||
| 5 | No digital (25, m, 115)-net over F5 with unbounded m | [i] | ||