Information on Result #598740
There is no digital (83, 167, 178)-net over F2, because extracting embedded orthogonal array would yield linear OA(2167, 178, F2, 84) (dual of [178, 11, 85]-code), but
- residual code [i] would yield linear OA(283, 93, F2, 42) (dual of [93, 10, 43]-code), but
- residual code [i] would yield linear OA(241, 50, F2, 21) (dual of [50, 9, 22]-code), but
- 1 times truncation [i] would yield linear OA(240, 49, F2, 20) (dual of [49, 9, 21]-code), but
- residual code [i] would yield linear OA(241, 50, F2, 21) (dual of [50, 9, 22]-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 (83, 168, 178)-net over F2 | [i] | m-Reduction | |
| 2 | No digital (83, 169, 178)-net over F2 | [i] | ||
| 3 | No digital (83, 170, 178)-net over F2 | [i] | ||