Information on Result #1849791
There is no (126, m, 137)-net in base 2 for arbitrarily large m, because m-reduction would yield (126, 949, 137)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2949, 137, S2, 7, 823), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 566256 038748 339790 313502 199295 482133 297983 884791 897410 008437 924027 510202 246681 985446 000094 160136 338304 595354 019305 484137 613106 061503 500093 526748 285283 791873 498155 296042 392719 997374 984864 900578 200187 085753 919427 288070 598707 579096 737570 223276 484768 998010 986776 156938 002003 289844 828631 728128 / 103 > 2949 [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 (126, 136)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (126, 126+k, 137)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (126, m, 137)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (126, 126+k, 137)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (126, m, 137)-net over F2 with unbounded m | [i] | ||