Information on Result #1849899
There is no (162, m, 173)-net in base 2 for arbitrarily large m, because m-reduction would yield (162, 1374, 173)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21374, 173, S2, 8, 1212), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 559 079710 795581 503490 255379 757320 029736 346859 173601 528398 814855 719239 979837 164473 905762 005111 213593 630359 516346 709356 345010 590546 216949 691924 743511 170891 373193 218948 374815 142083 802024 600993 356446 081305 846322 657706 636476 351979 960358 267757 601865 188568 913506 859188 026023 590523 634277 408422 609221 590257 364376 418948 215047 281989 644755 002201 346627 269632 041711 130350 285331 720006 815202 410337 439700 132075 641152 966409 282968 879104 / 1213 > 21374 [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 (162, 172)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (162, 162+k, 173)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (162, m, 173)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (162, 162+k, 173)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (162, m, 173)-net over F2 with unbounded m | [i] | ||