ON BALANCED ARRAYS OF 2 SYMBOLS, STRENGTH 2l, m CONSTRAINTS AND INDEX SET {μ₀, μ₁, …, μ_2l} WITH μ_l=0

Abstract

Consider a balanced array (“partially balanced” array, in the terminology of Chakravarti [1]) of 2 symbols, strength 2l, m constraints and index set {μ₀, μ₁, …, μ_2l}. Then it is shown that balanced arrays with μ_l=0 are simple. A necessary and sufficient condition for the existence of such balanced arrays is given.