Information on Result #598855
There is no digital (117, 237, 247)-net over F2, because extracting embedded orthogonal array would yield linear OA(2237, 247, F2, 120) (dual of [247, 10, 121]-code), but
- residual code [i] would yield linear OA(2117, 126, F2, 60) (dual of [126, 9, 61]-code), but
- residual code [i] would yield linear OA(257, 65, F2, 30) (dual of [65, 8, 31]-code), but
- 2 times truncation [i] would yield linear OA(255, 63, F2, 28) (dual of [63, 8, 29]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- 2 times truncation [i] would yield linear OA(255, 63, F2, 28) (dual of [63, 8, 29]-code), but
- residual code [i] would yield linear OA(257, 65, F2, 30) (dual of [65, 8, 31]-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 (117, 238, 247)-net over F2 | [i] | m-Reduction | |
| 2 | No digital (117, 239, 247)-net over F2 | [i] | ||
| 3 | No digital (117, 240, 247)-net over F2 | [i] | ||