On the norm of alias matrices in balanced fractional 2 m factorial designs of resolution 2 l + 1

Abstract

The norm ‖A‖ = {tr(A′A)} 1 2 of the alias matrix A of a design can be used as a measure for selecting a design. In this paper, an explicit expression for ‖ A‖ will be given for a balanced fractional 2 m factorial design of resolution 2 l + 1 which obtained from a simple array with parameters ( m; λ 0, λ 1,…, λ m ). This array is identical with a balanced array of strength m, m constraints and index set { λ 0, λ 1,…, λ m }. In the class of the designs of resolution V ( l = 2) obtained from S-arrays, ones which minimize ‖ A‖ will be presented for any fixed N assemblies satisfying (i) m = 4, 11 ⩽ N ⩽ 16, (ii) m = 5, 16 ⩽ N ⩽ 32, and (iii) m = 6, 22 ⩽ N ⩽ 40.