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Combining some difference methods with the famous Bays-Lambossy theorem and its generalizations we establish some non-trivial lower bounds on the number of cyclic 2-(v,k,1) designs up to isomorphism.

We present some results on the harmonious colourings of the Levi graph of a 2-design, focusing on Steiner 2-design. It is easily seen that the harmonious chromatic number of such a Levi graph is at least the number of points of the design: we study and construct Banff designs, that is designs such t ...