On STDk3[k;3]’s

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 STD3[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 STDk3[k;3] which admits an automorphism group acting regularly on the point groups and on the block groups respectively can only exist for k=3,9,12,21k=3,9,12,21, if k≤21k≤21, with the aid of a computer. In particular, the STD7[21;3] yields a new (21,3,21,7)(21,3,21,7)-semi-regular relative difference set.