Information on Result #520473
There is no (51, 107, 113)-net in base 2, because extracting embedded orthogonal array would yield OA(2107, 113, S2, 56), but
- adding a parity check bit [i] would yield OA(2108, 114, S2, 57), but
- the (dual) Plotkin bound shows that M ≥ 10384 593717 069655 257060 992658 440192 / 29 > 2108 [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 (51, 108, 113)-net in base 2 | [i] | m-Reduction | |
| 2 | No (51, 109, 113)-net in base 2 | [i] | ||
| 3 | No (51, 110, 113)-net in base 2 | [i] | ||
| 4 | No (51, 111, 113)-net in base 2 | [i] | ||
| 5 | No (51, 112, 113)-net in base 2 | [i] | ||
| 6 | No (51, 113, 113)-net in base 2 | [i] | ||
| 7 | No (51, 114, 113)-net in base 2 | [i] | ||