Information on Result #598744
There is no digital (84, 164, 189)-net over F2, because extracting embedded orthogonal array would yield linear OA(2164, 189, F2, 80) (dual of [189, 25, 81]-code), but
- residual code [i] would yield linear OA(284, 108, F2, 40) (dual of [108, 24, 41]-code), but
- adding a parity check bit [i] would yield linear OA(285, 109, F2, 41) (dual of [109, 24, 42]-code), but
- “Bro†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(285, 109, F2, 41) (dual of [109, 24, 42]-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, 165, 189)-net over F2 | [i] | m-Reduction | |