<p>In experimental designs, particularly block designs, when the response to a treatment is influenced by treatments applied to neighboring plots, interference models become essential. For these models, neighbor balanced designs have been proposed, typically under the condition that the block size (k) does not exceed the number of treatments (t). In certain experiments, particularly in agriculture and forestry, the block size can be so large that it exceeds the number of treatments. This paper focuses on interference models with k&gt;t. We introduce generalized neighbor balanced designs for the case k&gt;t and establish their universal optimality under various interference models. Furthermore, we present methods for constructing these optimal designs for all combinations of k and t where k&gt;t.</p>