Information on Result #1856420
There is no (81, 90)-sequence in base 2, because net from sequence would yield (81, m, 91)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (81, 628, 91)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2628, 91, S2, 7, 547), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 183789 722145 425344 500926 102280 407243 312349 292894 534274 547257 511097 016699 850935 490423 211819 791837 470938 348628 193272 235646 060458 075934 313298 269455 351014 200522 720112 090153 672782 413006 406670 090240 / 137 > 2628 [i]
- extracting embedded OOA [i] would yield OOA(2628, 91, S2, 7, 547), 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 (81, 90)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (81, m, 90)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (81, 90)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (81, m, 90)-net over F2 with m > ∞ | [i] | ||