Information on Result #1856471
There is no (132, 142)-sequence in base 2, because net from sequence would yield (132, m, 143)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (132, 991, 143)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2991, 143, S2, 7, 859), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 729705 961408 133096 373907 443116 414241 931200 926668 956939 107179 448666 002686 606163 353192 633468 991157 498766 335860 925136 937158 052633 487626 229958 071317 445081 792784 549242 806856 008208 408521 212390 812261 844565 713215 993170 598221 716262 562737 242912 915882 448078 552134 942195 228825 253693 861605 377916 233252 360314 421248 / 215 > 2991 [i]
- extracting embedded OOA [i] would yield OOA(2991, 143, S2, 7, 859), 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 (132, 142)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (132, m, 142)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (132, 142)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (132, m, 142)-net over F2 with m > ∞ | [i] | ||