  Optimal block designs in small blocks are explored when the treatments have a
natural ordering and interest lies in comparing consecutive pairs of
treatments. We first develop an approximate theory which leads to a convenient
multiplicative algorithm for obtaining optimal design measures. This, in turn,
yields highly efficient exact designs even when the number of blocks is rather
small. Moreover, our approach is seen to allow nesting of such efficient exact
designs which is an advantage when the resources for the experiment are
available possibly in several stages. Illustrative examples are given. Tables
of optimal design measures are also provided.
