Information on Result #1849797
There is no (128, m, 139)-net in base 2 for arbitrarily large m, because m-reduction would yield (128, 963, 139)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2963, 139, S2, 7, 835), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18243 227829 340798 278421 531830 102352 517960 296677 417854 090296 720887 902639 949114 749663 815631 403331 123205 269770 803185 197026 839435 565987 660192 055193 992218 697287 201362 551854 318517 511918 118235 077380 429716 440838 993096 805251 539439 316339 205898 437192 688157 903627 213527 039411 207568 137183 120464 863215 747072 / 209 > 2963 [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 (128, 138)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (128, 128+k, 139)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (128, m, 139)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (128, 128+k, 139)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (128, m, 139)-net over F2 with unbounded m | [i] | ||