Information on Result #1849758
There is no (115, m, 126)-net in base 2 for arbitrarily large m, because m-reduction would yield (115, 872, 126)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2872, 126, S2, 7, 757), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 16 374180 089863 892084 551852 235590 734207 022226 425336 789578 589175 265662 099679 082448 895376 740280 484064 680649 679028 778893 167556 453986 820065 765343 325154 113812 958001 635138 730971 970782 741331 409915 789922 927177 018658 507941 374598 426355 767971 527336 024484 566388 593587 879065 681920 / 379 > 2872 [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 (115, 125)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (115, 115+k, 126)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (115, m, 126)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (115, 115+k, 126)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (115, m, 126)-net over F2 with unbounded m | [i] | ||