Information on Result #1856250
There is no (14, m, 54)-net in base 4 for arbitrarily large m, because m-reduction would yield (14, 158, 54)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4158, 54, S4, 3, 144), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 24 563850 913090 465947 542749 620949 849317 931102 007101 506854 390978 489955 526846 477366 325264 063999 770624 / 145 > 4158 [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 (14, 53)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (14, 14+k, 54)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (14, m, 54)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (14, 14+k, 54)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (14, m, 54)-net over F4 with unbounded m | [i] | ||