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The existence of blocking sets in (v, {2, 4}, 1)-designs is examined. We show that for v ≡ 0, 3, 5, 6, 7, 8, 9, 11 (mod 12), blocking sets cannot exist. We prove that for each v ≡ 1, 2, 4 (mod 12) there is a (v, {2, 4}, 1)-design with a blocking set with three possible exceptions. The case v ≡ 10 (mod 12) is still open; we consider the first four values of… (More)

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges. 1 Background information In any combinatorial connguration it is possible to identify a subset which uniquely determines the structure of… (More)

It is shown that in some cases it is possible to reconstruct a block design D uniquely from incomplete knowledge of a minimal defining set for D. This surprising result has implications for the use of minimal defining sets in secret sharing schemes.