Information on Result #1856353
There is no (14, 21)-sequence in base 2, because net from sequence would yield (14, m, 22)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (14, 80, 22)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(280, 22, S2, 4, 66), but
- the LP bound with quadratic polynomials shows that M ≥ 83 718113 008313 070348 402688 / 67 > 280 [i]
- extracting embedded OOA [i] would yield OOA(280, 22, S2, 4, 66), 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 (14, 21)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (14, m, 21)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (14, 21)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (14, m, 21)-net over F2 with m > ∞ | [i] | ||