Information on Result #1849638
There is no (75, m, 85)-net in base 2 for arbitrarily large m, because m-reduction would yield (75, 586, 85)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2586, 85, S2, 7, 511), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 338 347989 215207 002594 767448 754877 355968 059685 570457 797002 438260 735083 403945 735594 288992 836651 780485 545769 614510 790078 616232 667366 931635 655235 603140 179389 853709 918064 299420 418048 > 2586 [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 (75, 84)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (75, 75+k, 85)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (75, m, 85)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (75, 75+k, 85)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (75, m, 85)-net over F2 with unbounded m | [i] | ||