Information on Result #1857278
There is no (15, 107)-sequence in base 7, because net from sequence would yield (15, m, 108)-net in base 7 for arbitrarily large m, but
- m-reduction [i] would yield (15, 213, 108)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7213, 108, S7, 2, 198), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 219 959263 521121 203458 445918 825688 631593 444842 427135 365322 015188 309591 612642 274535 896532 994272 053854 562239 434041 618006 652422 484902 485444 974825 620207 788621 610341 301138 150263 852377 538319 / 199 > 7213 [i]
- extracting embedded OOA [i] would yield OOA(7213, 108, S7, 2, 198), but
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 (15, 107)-sequence in base 7 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (15, m, 107)-net in base 7 with m > ∞ | [i] | ||
| 3 | No digital (15, 107)-sequence over F7 (for arbitrarily large k) | [i] | ||
| 4 | No digital (15, m, 107)-net over F7 with m > ∞ | [i] | ||