Information on Result #1856468
There is no (129, 139)-sequence in base 2, because net from sequence would yield (129, m, 140)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (129, 970, 140)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2970, 140, S2, 7, 841), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 630349 518120 549963 042784 694245 465473 276486 924210 261496 285909 602454 331589 135996 632621 102479 942914 826527 274476 678526 588966 016056 133073 137292 914878 572020 808895 142413 161246 518769 520687 513750 922130 263755 787647 341903 664527 480255 880419 302222 144222 799462 445416 520503 951754 016610 271708 934398 103032 692736 / 421 > 2970 [i]
- extracting embedded OOA [i] would yield OOA(2970, 140, S2, 7, 841), 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 (129, 139)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (129, m, 139)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (129, 139)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (129, m, 139)-net over F2 with m > ∞ | [i] | ||