Partially Balanced t-designs with Unequal Block Sizes

Abstract

An amalgamation of crop and livestock in Integrated Farming System (IFS) approach is most preferred by small and marginal farmers in India as it helps them to generate a stable income all the year round. Therefore, the best crop-livestock combination for a particular location needs to be identified that will help them in generating maximum profit. t-designs can be advantageously used in identifying those combinations. However, all possible crop-livestock combinations may not be feasible, as number of combinations increases drastically as the number of components increases. Partially balanced t-designs, with few selected combinations may prove to be useful in those situations. Further, every location may not have the resources to form equally sized homogeneous blocks. Partially balanced t-designs with unequal block sizes find high application potential in such situations. Here, a series of partially balanced t-designs with unequal block sizes have been obtained utilizing the triangular association scheme. Some interesting characterization properties for the developed designs have been also studied.