Information on Result #1856464
There is no (125, 135)-sequence in base 2, because net from sequence would yield (125, m, 136)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (125, 942, 136)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2942, 136, S2, 7, 817), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 17844 202901 733396 753576 749977 798806 721575 122419 912733 508669 262311 791287 885924 852482 542019 773953 876207 077584 685482 315676 605455 022946 538868 493489 966973 228735 509395 650085 369518 487312 236918 011572 842442 870349 388217 246472 812984 482534 561057 885187 284183 896996 144541 265449 726953 885184 185776 209920 / 409 > 2942 [i]
- extracting embedded OOA [i] would yield OOA(2942, 136, S2, 7, 817), 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 (125, 135)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (125, m, 135)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (125, 135)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (125, m, 135)-net over F2 with m > ∞ | [i] | ||