Information on Result #1856417
There is no (78, 87)-sequence in base 2, because net from sequence would yield (78, m, 88)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (78, 607, 88)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2607, 88, S2, 7, 529), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 178462 365586 433745 159701 637401 629458 782743 287556 282726 195013 230435 335596 113246 353560 358600 761117 039984 746814 707378 824341 156450 657451 309632 441598 712865 573350 253127 307000 692121 594660 651008 / 265 > 2607 [i]
- extracting embedded OOA [i] would yield OOA(2607, 88, S2, 7, 529), but
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 (78, 87)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (78, m, 87)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (78, 87)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (78, m, 87)-net over F2 with m > ∞ | [i] | ||