Balanced ternary designs from any \((v, b, r, k)\) design (Q2761059)

For a block of a \((v,b,r,k)\)-design consider sets of size \(v-1\) that contain the block. There are \(v-k\) such sets, and for each of them consider \(v-1\) multisets in which one point is counted twice. In this way one gets \(b(v-1)(v-k)=v(b-r)(v-1)\) multisets, and it turns out that when these multisets are regarded as blocks, they form a \((V,B,R,K,\Lambda)\) balanced ternary design with \(V=K=v\), \(B=R=v(b-r)(v-1)\), and \(\Lambda =(v+1)(v-2)(v-r)\). The paper contains several further results of this kind. There are quite a few misprints and the exposition is not always clear.