On \(STD_{\frac{k}{3}}[k;3]\)'s
A \textsl{transversal design} TD\(_\lambda[k;u]\) is a set of \(ku\) points \(V\) partitioned into \(k\) classes (or groups) each of size \(u\) and a collection \(\mathcal B\) of \(k\)-subsets of \(V\) called blocks for which (1) no pair of points from the same class is a subset of a block and (2) every pair of points from different classes is a subset of exactly \(\lambda\) of the blocks. It is a \textsl{symmetric transversal design} STD\(_\lambda[k;u]\) if, in addition, the dual structure forms a TD\(_\lambda[k;u]\), and hence \(k = \lambda u\). In this paper, the existence of STD\(_{k/3}[k;3]\)s that admit an automorphism acting regularly on the point groups and on the block groups are studied. A computer search is undertaken for \(k \leq 21\) and properties of the designs are reported.
scientific article; zbMATH DE number 5499784