Information on Result #1849815
There is no (134, m, 145)-net in base 2 for arbitrarily large m, because m-reduction would yield (134, 1005, 145)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(21005, 145, S2, 7, 871), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 38059 985727 256215 240088 057742 611264 311141 098911 780553 736402 013794 914869 335957 731070 958406 415533 516880 692162 782031 487775 230647 400547 790994 828617 219545 329337 703575 584736 175668 460215 656997 181542 295950 493255 007621 079141 683055 381800 422370 156012 096465 727472 556889 888742 597779 529846 762030 121822 045754 532982 423552 / 109 > 21005 [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 (134, 144)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (134, 134+k, 145)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (134, m, 145)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (134, 134+k, 145)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (134, m, 145)-net over F2 with unbounded m | [i] | ||