Information on Result #1849785
There is no (124, m, 135)-net in base 2 for arbitrarily large m, because m-reduction would yield (124, 935, 135)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2935, 135, S2, 7, 811), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 70 284783 564770 215077 564672 764116 393662 454095 469057 316228 807966 787980 007623 597237 968345 846114 857390 008345 955304 145839 741837 892505 746458 433844 800976 684917 870984 273231 130524 470604 322287 339824 228969 257399 488150 204649 193045 934973 524801 041800 379602 417042 204866 194437 481020 879560 784065 069056 / 203 > 2935 [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 (124, 134)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (124, 124+k, 135)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (124, m, 135)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (124, 124+k, 135)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (124, m, 135)-net over F2 with unbounded m | [i] | ||