Information on Result #598630
There is no digital (53, 109, 117)-net over F2, because extracting embedded orthogonal array would yield linear OA(2109, 117, F2, 56) (dual of [117, 8, 57]-code), but
- 1 times code embedding in larger space [i] would yield linear OA(2110, 118, F2, 56) (dual of [118, 8, 57]-code), but
- adding a parity check bit [i] would yield linear OA(2111, 119, F2, 57) (dual of [119, 8, 58]-code), but
- “DMa†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(2111, 119, F2, 57) (dual of [119, 8, 58]-code), but
Mode: Bound (linear).
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 digital (53, 110, 117)-net over F2 | [i] | m-Reduction | |