Information on Result #1854609
There is no (4, m, 166)-net in base 32 for arbitrarily large m, because m-reduction would yield (4, 164, 166)-net in base 32, but
- extracting embedded OOA [i] would yield OA(32164, 166, S32, 160), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1342 448621 178513 806457 130496 891008 054252 581523 695499 337317 567954 795831 125250 917382 469310 199960 529455 098251 226994 640611 878487 352847 987814 532833 360595 698339 669711 540983 186525 567293 756309 131827 130136 486250 385863 058475 434244 700315 824231 969943 145615 982592 / 161 > 32164 [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 (4, 165)-sequence in base 32 | [i] | Net from Sequence | |
| 2 | No (4, 4+k, 166)-net in base 32 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (4, m, 166)-net in base 32 with unbounded m | [i] | ||
| 4 | No digital (4, 4+k, 166)-net over F32 for arbitrarily large k | [i] | ||
| 5 | No digital (4, m, 166)-net over F32 with unbounded m | [i] | ||