Information on Result #1849725
There is no (104, m, 115)-net in base 2 for arbitrarily large m, because m-reduction 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]
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 | [i] | Net from Sequence | |
| 2 | No (104, 104+k, 115)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (104, m, 115)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (104, 104+k, 115)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (104, m, 115)-net over F2 with unbounded m | [i] | ||