Information on Result #1849692
There is no (93, m, 103)-net in base 2 for arbitrarily large m, because m-reduction would yield (93, 815, 103)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2815, 103, S2, 8, 722), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 178 730952 494144 579049 793741 285293 715556 414662 497219 801094 689223 148273 089266 805081 194644 489512 974136 437234 619739 846357 505957 463318 628585 984351 837397 018431 290661 464929 076591 457364 305446 105116 307365 176717 580669 918918 116082 709124 079463 175685 789894 836224 / 723 > 2815 [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 (93, 102)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (93, 93+k, 103)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (93, m, 103)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (93, 93+k, 103)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (93, m, 103)-net over F2 with unbounded m | [i] | ||