Information on Result #598556
There is no digital (25, 49, 60)-net over F2, because extracting embedded orthogonal array would yield linear OA(249, 60, F2, 24) (dual of [60, 11, 25]-code), but
- construction Y1 [i] would yield
- linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-code), but
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(249, 57, F2, 25) (dual of [57, 8, 26]-code), but
- linear OA(211, 60, F2, 4) (dual of [60, 49, 5]-code), but
- discarding factors / shortening the dual code would yield linear OA(211, 58, F2, 4) (dual of [58, 47, 5]-code), but
- construction Y1 [i] would yield
- linear OA(210, 34, F2, 4) (dual of [34, 24, 5]-code), but
- “BoV†bound on codes from Brouwer’s database [i]
- linear OA(247, 58, F2, 24) (dual of [58, 11, 25]-code), but
- discarding factors / shortening the dual code would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), but
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- “vT4†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(248, 55, F2, 25) (dual of [55, 7, 26]-code), but
- discarding factors / shortening the dual code would yield linear OA(247, 54, F2, 24) (dual of [54, 7, 25]-code), but
- linear OA(210, 34, F2, 4) (dual of [34, 24, 5]-code), but
- construction Y1 [i] would yield
- discarding factors / shortening the dual code would yield linear OA(211, 58, F2, 4) (dual of [58, 47, 5]-code), but
- linear OA(248, 56, F2, 24) (dual of [56, 8, 25]-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 (25, 50, 60)-net over F2 | [i] | m-Reduction | |