Information on Result #599699
There is no digital (2, 7, 42)-net over F5, because extracting embedded orthogonal array would yield linear OA(57, 42, F5, 5) (dual of [42, 35, 6]-code), but
- construction Y1 [i] would yield
- linear OA(56, 13, F5, 5) (dual of [13, 7, 6]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(57, 13, F5, 6) (dual of [13, 6, 7]-code), but
- discarding factors / shortening the dual code would yield linear OA(57, 12, F5, 6) (dual of [12, 5, 7]-code), but
- dual of a near-MDS code is again a near-MDS code [i] would yield linear OA(57, 13, F5, 6) (dual of [13, 6, 7]-code), but
- linear OA(535, 42, F5, 29) (dual of [42, 7, 30]-code), but
- discarding factors / shortening the dual code would yield linear OA(535, 41, F5, 29) (dual of [41, 6, 30]-code), but
- “DG1†bound on codes from Brouwer’s database [i]
- discarding factors / shortening the dual code would yield linear OA(535, 41, F5, 29) (dual of [41, 6, 30]-code), but
- linear OA(56, 13, F5, 5) (dual of [13, 7, 6]-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
None.