Information on Result #1849737
There is no (108, m, 119)-net in base 2 for arbitrarily large m, because m-reduction would yield (108, 823, 119)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2823, 119, S2, 7, 715), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 15326 288425 121365 957052 239839 505675 286050 305728 856950 767708 900817 252405 346614 640116 524624 782882 711279 038368 174855 480318 946063 945014 527549 249847 533467 556044 562540 092891 379500 226603 717862 588359 735724 884691 905269 917594 540960 328605 659981 656850 912449 134592 / 179 > 2823 [i]
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 (108, 118)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (108, 108+k, 119)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (108, m, 119)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (108, 108+k, 119)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (108, m, 119)-net over F2 with unbounded m | [i] | ||