Information on Result #1850925
There is no (44, m, 147)-net in base 4 for arbitrarily large m, because m-reduction would yield (44, 583, 147)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(4583, 147, S4, 4, 539), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 23051 690513 784546 883284 910989 995732 444940 266964 568283 187683 232057 444811 559896 924838 315587 511543 944826 441964 317214 158161 027441 577036 444982 721866 517519 971850 498531 047478 788985 769517 465821 697916 128314 609085 305029 299536 309598 547495 732306 708185 736722 850208 689297 249191 847019 272117 614688 010173 752935 240451 822820 747486 222137 478258 607515 184716 457444 710308 380672 / 15 > 4583 [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 (44, 146)-sequence in base 4 | [i] | Net from Sequence | |
| 2 | No (44, 44+k, 147)-net in base 4 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (44, m, 147)-net in base 4 with unbounded m | [i] | ||
| 4 | No digital (44, 44+k, 147)-net over F4 for arbitrarily large k | [i] | ||
| 5 | No digital (44, m, 147)-net over F4 with unbounded m | [i] | ||