A combinatorial theorem for a class of residual treatment effects designs

In this paper a combinatorial theorem for a class of residual treatment effects designs is proved. It is assumed that the number of treatments of a design in this class is a prime or a prime power. A method of constructions of the class of designs under consideration is given in detail. The theorem presented here gives complete information on the frequencies of occurrences of ordered pairs of treatments among various types of ordered pairs of treatments arising from the sequences of the design. The proof of the theorem is based on the properties of symmetrically repeated difference sets. © 1993

A combinatorial theorem for a class of residual treatment effects designs

In this paper a combinatorial theorem for a class of residual treatment effects designs is proved. It is assumed that the number of treatments of a design in this class is a prime or a prime power. A method of constructions of the class of designs under consideration is given in detail. The theorem presented here gives complete information on the frequencies of occurrences of ordered pairs of treatments among various types of ordered pairs of treatments arising from the sequences of the design. The proof of the theorem is based on the properties of symmetrically repeated difference sets.Combinatorially balanced design difference sets residual treatment effects Galios field