  The maximum size $A_2(8,6;4)$ of a binary subspace code of packet length
$v=8$, minimum subspace distance $d=6$, and constant dimension $k=4$ is $257$,
where the $2$ isomorphism types are extended lifted maximum rank distance
codes. In finite geometry terms the maximum number of solids in
$\operatorname{PG}(7,2)$, mutually intersecting in at most a point, is $257$.
The result was obtained by combining the classification of substructures with
integer linear programming techniques. This implies that the maximum size
$A_2(8,6)$ of a binary mixed-dimension code of packet length $8$ and minimum
subspace distance $6$ is $257$ as well.
