Information on Result #1856443
There is no (104, 114)-sequence in base 2, because net from sequence would yield (104, m, 115)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (104, 681, 115)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2681, 115, S2, 6, 577), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3090 137210 229681 091747 712867 597731 836298 951452 769351 098490 658794 679965 025946 618830 129641 138407 701955 753156 193557 172567 473621 340051 758979 015051 587961 885031 322071 473866 858598 587499 680399 758093 637313 000338 620416 / 289 > 2681 [i]
- extracting embedded OOA [i] would yield OOA(2681, 115, S2, 6, 577), 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 (104, 114)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (104, m, 114)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (104, 114)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (104, m, 114)-net over F2 with m > ∞ | [i] | ||