A subspace $t$ -design with parameters $t$ - $(v,k,\lambda _{t})_{q}$ is a pair $\mathcal{D}=(\mathcal{V}, \mathcal{B})$ where $\mathcal{V}$ is the $v$ -dimensional vector space over the field $\mathbb{F}_{q}$ , and ℬ is a collection of $k$ -dimensional subspaces of $\mathcal{V}$ such that every $t$ -dimensional subspace of $\mathcal{V}$ is contained in precisely $\lambda _{t}$ members of ℬ. In this paper, we give new general necessary conditions for the existence of a subspace 3-design $\mathcal{D}$ with a prescribed automorphism group $G$ . These necessary conditions are based on a tactical decomposition of $\mathcal{D}$ induced by the action of $G$ and are given by means of a system of equations involving the coefficients of the tactical decomposition matrices.
