Information on Result #598655
There is no digital (67, 135, 144)-net over F2, because extracting embedded orthogonal array would yield linear OA(2135, 144, F2, 68) (dual of [144, 9, 69]-code), but
- residual code [i] would yield linear OA(267, 75, F2, 34) (dual of [75, 8, 35]-code), but
- adding a parity check bit [i] would yield linear OA(268, 76, F2, 35) (dual of [76, 8, 36]-code), but
- “BJV†bound on codes from Brouwer’s database [i]
- adding a parity check bit [i] would yield linear OA(268, 76, F2, 35) (dual of [76, 8, 36]-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 (67, 136, 144)-net over F2 | [i] | m-Reduction | |
| 2 | No digital (67, 137, 144)-net over F2 | [i] | ||
| 3 | No digital (67, 138, 144)-net over F2 | [i] | ||
| 4 | No digital (67, 139, 144)-net over F2 | [i] | ||
| 5 | No digital (67, 140, 144)-net over F2 | [i] | ||
| 6 | No digital (67, 141, 144)-net over F2 | [i] | ||
| 7 | No digital (67, 142, 144)-net over F2 | [i] | ||
| 8 | No digital (67, 143, 144)-net over F2 | [i] | ||
| 9 | No digital (67, 144, 144)-net over F2 | [i] | ||
| 10 | No digital (67, 145, 144)-net over F2 | [i] | ||
| 11 | No digital (67, 146, 144)-net over F2 | [i] | ||
| 12 | No digital (67, 147, 144)-net over F2 | [i] | ||
| 13 | No digital (67, 148, 144)-net over F2 | [i] | ||
| 14 | No digital (67, 149, 144)-net over F2 | [i] | ||
| 15 | No digital (67, 150, 144)-net over F2 | [i] | ||
| 16 | No digital (67, 151, 144)-net over F2 | [i] | ||
| 17 | No digital (67, 152, 144)-net over F2 | [i] | ||