Additivity of symmetric and subspace 2-designs

A 2- (v,k,λ ) ( v , k , λ ) 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.