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Abstract A 2- (v, k, ) (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.
Buratti et al. (Fri,) studied this question.