On a class of partially balanced incomplete block designs with applications in survey sampling
We revisit the existence and construction problems of balanced sampling plans excluding contiguous units, a class of designs introduced and studied by Hedayat, Rao, and Stufken (1988a,b). A link between these designs and a class of partially balanced incomplete block designs is established, and a Fisher-type inequality is shown to hold. Special attention is given to those designs that attain equality in this Fisher-type inequality. Some new designs are obtained by construction, while the nonexistence of designs is considered for some other sets of parameters.