Kerr and Churchill ( Biostatistics 2001; 2 :183–201) showed how varieties (e.g. type of tissues, drug treatments, etc.) are paired onto arrays by a catalogue of A-optimal incomplete block designs (IBDs) for 6–10 varieties ( v ), and number of blocks of size 2 between v and $ ≤ft(v \atop 2 \right)$. These A-optimal IBDs were obtained by (i) generating all non-isomorphic connected graphs on v vertices using Brendan McKay's, MAKEG program () and (ii) comparing all designs of the same size on the basis of A-optimality to obtain the best ones.In this paper we will give a quick overview on IBDs and describe an algorithmic approach to extend the mentioned catalogue. We aim at IBDs with up to 100 varieties with equal as well as unequal replications. A catalogue of 2007 IBDs is given. We will also extend the concept of even designs in Kerr and Churchill ( Biostatistics 2001; 2 :183–201) to row-orthogonal designs. Copyright © 2006 John Wiley & Sons, Ltd.