Information on Result #1849680
There is no (89, m, 99)-net in base 2 for arbitrarily large m, because m-reduction would yield (89, 684, 99)-net in base 2, but
- extracting embedded OOA [i] would yield OOA(2684, 99, S2, 7, 595), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12601 338753 404154 062451 712213 320620 735037 282547 656834 349689 180019 863753 482431 666398 191004 122857 382001 383000 581518 859560 866455 854237 043109 230210 371688 725971 884810 945379 137661 772401 294097 714823 404107 559822 426112 / 149 > 2684 [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 (89, 98)-sequence in base 2 | [i] | Net from Sequence | |
| 2 | No (89, 89+k, 99)-net in base 2 for arbitrarily large k | [i] | Logical Equivalence (for Nets with Unbounded m) | |
| 3 | No (89, m, 99)-net in base 2 with unbounded m | [i] | ||
| 4 | No digital (89, 89+k, 99)-net over F2 for arbitrarily large k | [i] | ||
| 5 | No digital (89, m, 99)-net over F2 with unbounded m | [i] | ||