Additivity of symmetric and subspace 2-designs

A 2- \((v,k,\lambda )\) $(v,k,\lambda )$ design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of PG \(_d(n,q)\) $_d^{}(n,q)$ , which was known to be additive only for \(q=2\) $q=2$ or \(d=n-1\) $d=n-1$ , is always established.