Information on Result #1852026
There is no (18, m, 127)-net in base 7 for arbitrarily large m, because m-reduction would yield (18, 251, 127)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(7251, 127, S7, 2, 233), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1843 894543 978382 470179 249159 079505 153821 338650 778903 015340 580083 735697 604338 184087 336945 800781 291445 883210 708256 820164 597140 660912 903423 585885 904095 278589 303582 845345 588601 810631 609107 463290 896513 324650 720226 862402 / 13 > 7251 [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 (18, 126)-sequence in base 7 | [i] | Net from Sequence | |
| 2 | No (18, 18+k, 127)-net in base 7 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (18, m, 127)-net in base 7 with unbounded m | [i] | ||
| 4 | No digital (18, 18+k, 127)-net over F7 for arbitrarily large k | [i] | ||
| 5 | No digital (18, m, 127)-net over F7 with unbounded m | [i] | ||