Abstract
This chapter presents combinatorial properties of partially balanced designs and association schemes. Partially balanced designs were first introduced in 1939 as an extension of the balanced incomplete block (BIB) and lattice designs. The definition of partially balanced incomplete block (PBIB) designs has been generalized, so as to include as special cases the cubic and other higher dimensional lattices. The concept of association schemes have been introduced, and basing the definition PBIB design on these schemes. The chapter discusses the group divisible (GD) association scheme and the triangular association scheme.
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