Information on Result #520637
There is no (84, 174, 180)-net in base 2, because extracting embedded orthogonal array would yield OA(2174, 180, S2, 90), but
- adding a parity check bit [i] would yield OA(2175, 181, S2, 91), but
- the (dual) Plotkin bound shows that M ≥ 1 149371 655649 416643 768760 270362 731887 714054 341637 701632 / 23 > 2175 [i]
Mode: Bound.
Optimality
Show details for fixed k and m, k and s, k and t, 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 (84, 175, 180)-net in base 2 | [i] | m-Reduction | |
| 2 | No (84, 176, 180)-net in base 2 | [i] | ||
| 3 | No (84, 177, 180)-net in base 2 | [i] | ||
| 4 | No (84, 178, 180)-net in base 2 | [i] | ||
| 5 | No (84, 179, 180)-net in base 2 | [i] | ||
| 6 | No (84, 180, 180)-net in base 2 | [i] | ||
| 7 | No (84, 181, 180)-net in base 2 | [i] | ||
| 8 | No (84, 182, 180)-net in base 2 | [i] | ||
| 9 | No (84, 183, 180)-net in base 2 | [i] | ||
| 10 | No (84, 184, 180)-net in base 2 | [i] | ||
| 11 | No (84, 185, 180)-net in base 2 | [i] | ||
| 12 | No (84, 186, 180)-net in base 2 | [i] | ||
| 13 | No (84, 187, 180)-net in base 2 | [i] | ||