Information on Result #1856456
There is no (117, 127)-sequence in base 2, because net from sequence would yield (117, m, 128)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (117, 886, 128)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2886, 128, S2, 7, 769), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 264147 265567 832623 176169 892458 258303 259423 663018 060761 063980 354513 336951 278362 429737 208627 943828 593947 337197 496628 564339 441173 779751 342768 625269 489231 469788 454193 341999 502542 084365 758838 213220 526512 116454 105594 202074 014146 375780 869419 198449 383518 238244 769290 448868 999168 / 385 > 2886 [i]
- extracting embedded OOA [i] would yield OOA(2886, 128, S2, 7, 769), 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 (117, 127)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (117, m, 127)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (117, 127)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (117, m, 127)-net over F2 with m > ∞ | [i] | ||