  We propose a novel model-based approach for constructing optimal designs with
complex blocking structures and network effects, for application in
agricultural field experiments. The potential interference among treatments
applied to different plots is described via a network structure, defined via
the adjacency matrix. We consider a field trial run at Rothamsted Research and
provide a comparison of optimal designs under various different models,
including the commonly used designs in such situations. It is shown that when
there is interference between treatments on neighbouring plots, due to the
spatial arrangement of the plots, designs incorporating network effects are at
least as, and often more efficient than, randomised row-column designs. The
advantage of network designs is that we can construct the neighbour structure
even for an irregular layout by means of a graph to address the particular
characteristics of the experiment. The need for such designs arises when it is
required to account for treatment-induced patterns of heterogeneity. Ignoring
the network structure can lead to imprecise estimates of the treatment
parameters and invalid conclusions.
