Information on Result #598638
There is no digital (59, 119, 129)-net over F2, because extracting embedded orthogonal array would yield linear OA(2119, 129, F2, 60) (dual of [129, 10, 61]-code), but
- residual code [i] would yield linear OA(259, 68, F2, 30) (dual of [68, 9, 31]-code), but
- adding a parity check bit [i] would yield linear OA(260, 69, F2, 31) (dual of [69, 9, 32]-code), but
- “BGV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(260, 69, F2, 31) (dual of [69, 9, 32]-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 (59, 120, 129)-net over F2 | [i] | m-Reduction | |
| 2 | No digital (59, 121, 129)-net over F2 | [i] | ||
| 3 | No digital (59, 122, 129)-net over F2 | [i] | ||