Information on Result #1856260
There is no (24, m, 86)-net in base 4 for arbitrarily large m, because m-reduction would yield (24, 254, 86)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4254, 86, S4, 3, 230), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 87150 751544 626881 147231 162488 337999 828615 877833 850556 955203 149384 191466 195478 055349 212182 938084 872279 985207 078212 159330 549400 238277 652704 651818 718539 546624 / 77 > 4254 [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 (24, 85)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (24, 24+k, 86)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (24, m, 86)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (24, 24+k, 86)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (24, m, 86)-net over F4 with unbounded m | [i] | ||