Information on Result #598746
There is no digital (84, 168, 180)-net over F2, because extracting embedded orthogonal array would yield linear OA(2168, 180, F2, 84) (dual of [180, 12, 85]-code), but
- residual code [i] would yield linear OA(284, 95, F2, 42) (dual of [95, 11, 43]-code), but
- adding a parity check bit [i] would yield linear OA(285, 96, F2, 43) (dual of [96, 11, 44]-code), but
- “Bro†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(285, 96, F2, 43) (dual of [96, 11, 44]-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 (84, 169, 180)-net over F2 | [i] | m-Reduction | |
| 2 | No digital (84, 170, 180)-net over F2 | [i] | ||
| 3 | No digital (84, 171, 180)-net over F2 | [i] | ||