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V. C. Mavron and V. D. Tonchev [V.C. Mavron, V.D. Tonchev, On symmetric nets and generalized Hadamard matrices from affine designs, J. Geom. 67 (2000) 180-187] constructed a symmetric transversal design STD"3[9;3] which admits an automorphism group acting regularly on the point groups and on the block groups respectively, but does not admit a class regular automorphism group. We construct many symmetric transversal designs of class size 3 with such a property. Also we show that an STD"k"3[k;3] which admits an automorphism group acting regularly on the point groups and on the block groups respectively can only exist for k=3,9,12,21, if k@?21, with the aid of a computer. In particular, the STD"7[21;3] yields a new (21,3,21,7)-semi-regular relative difference set. |
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