Universal optimal block designs under hub correlation structure

Universal optimal block designs under general correlation structures are usually difficult to specify theoretically or algorithmically. However, they can sometimes be found for a specific correlation and a particular parameter value.In this paper, a wide class of block designs, binary and non-binary with v treatments and b blocks each of size k is considered and we present a method to construct the universal optimal block designs under the hub correlation when, in this method, b is less than (or equal to) the number of blocks in semibalanced array methods.