Some New Families of Partially Balanced Designs of the Latin Square Type and Related Designs

Abstract

Four very general families of partially balanced incomplete block designs with two associate classes and having the Latin square type of association scheme are presented. These families have simple, yet general, constructions and the treatment extends particular solutions presented by Chang and Liu (1964). The general treatment brings out relations between the class studied and certain other closely related designs, including balanced incomplete block designs, regular and semi-regular group divisible designs, and various square lattice designs. A by-product is the discovery of one new L 3(5) type and four new regular group divisible designs.