Subspace code constructions

We improve on the lower bound of the maximum number of planes of ${\rm PG}(8,q)$ mutually intersecting in at most one point leading to the following lower bound: ${\cal A}q(9, 4; 3) \ge q^{{12}+2q8+2q7+q6+q5+q4+1$} for constant dimension subspace codes. We also construct two new non-equivalent $(6, (q^{3-1)(q2+q+1),} 4; 3)q$ constant dimension subspace orbit-codes.