Information on Result #1856469
There is no (130, 140)-sequence in base 2, because net from sequence would yield (130, m, 141)-net in base 2 for arbitrarily large m, but
- m-reduction [i] would yield (130, 977, 141)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2977, 141, S2, 7, 847), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 73 446923 390877 689068 954515 839755 659231 282206 384024 837527 293738 521689 397620 777877 620886 453130 128993 800087 802043 866283 824978 185717 972884 246715 201522 176881 796267 776208 764599 952895 845388 149152 557928 321643 528199 216402 954573 824748 448030 311109 873878 888024 996262 049373 027822 332438 792624 476659 565346 160640 / 53 > 2977 [i]
- extracting embedded OOA [i] would yield OOA(2977, 141, S2, 7, 847), 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 (130, 140)-sequence in base 2 (for arbitrarily large k) | [i] | Logical Equivalence (for Sequences) | |
| 2 | No (130, m, 140)-net in base 2 with m > ∞ | [i] | ||
| 3 | No digital (130, 140)-sequence over F2 (for arbitrarily large k) | [i] | ||
| 4 | No digital (130, m, 140)-net over F2 with m > ∞ | [i] | ||