Abstract: We describe a construction of sixty-seven symmetric (31,15,7) designs, thirty-eight symmetric (63,31,15) designs, and two symmetric (127,63,31) designs. The orders and the structures of the full automorphism groups of the constructed designs are given, as well as their 2-ranks. The designs are constructed with the help of tactical decompositions.
Keywords: Symmetric design, classical parameters, automorphism group, difference set.
Classification (MSC2000): 05B05
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