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Neighbor-balanced designs are used in the experiments where the performance of a treatment is affected by the treatments applied to its neighboring units. These are well-known designs to balance the neighbor effects. Among these designs, minimal neighbor-balanced designs are economical; therefore, these are preferred by the experimenters. For v even, minimal neighbor balanced designs in circular blocks cannot be constructed for most of the cases, where v is number of treatments. In such situations, experimenters would like to relax the neighbor balance property up to some extent and consider the minimal circular weakly balanced neighbor designs as the better alternates to the minimal circular neighbor-balanced designs. In this article, some generators are developed to obtain minimal circular weakly balanced neighbor designs in blocks of equal, two and three different sizes.

Neighbor designs are used in the experiments where neighbor effects may arise. Neighbor designs neutralize these effects and are, therefore, considered to be robust against neighbor effects. Minimal neighbor designs are always most economical among the neighbor designs and are, therefore, preferred by the experimenters. Method of cyclic shifts provides these designs in circular blocks only for odd v (number of treatments). For v even, minimal circular generalized neighbor designs in which only v 2 unordered pairs of distinct treatments do not appear as neighbors will be the better alternate to the minimal neighbor designs. In this article, such minimal generalized neighbor designs are constructed in circular blocks for v even.

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