Several 2-(46,6,3) designs
A t-(v,k,\(\lambda\)) design is a set of v points with a collection of k- subsets called blocks, so that any t points lie in exactly \(\lambda\) blocks. For \(t=2\) the design is the ordinary balanced incomplete block design (BIBD). Using the usual extension approach this paper provides a construction method for 2-(46,6,3) designs based on the unique generalized quadrangle H of order (4,2). This quadrangle can be realized as the totally singular points and lines of a Hermitian variety in PG(3,4). Apart from H itself two other structures are used, namely, a 5- edge colouring of \(K_ 5\) and a punctured projective plane of order 2. The construction results in a large class of non-isomorphic 2-(46,6,3) designs, which is a new result because only such design was known before. The author also presents designs for two related parameter sets. An interesting large class of non-isomorphic 2-(298,10,5) designs is given with the author's query that does not know of any previous construction of such a design.
scientific article; zbMATH DE number 4191643