Abstract
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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