Characteristic polynomials of the information matrices of balanced fractional 3m factorial designs of resolution v

An explicit expression for the characteristic polynomial of the information matrix M_T of a balanced fractional 3^m factorial (3^m-BFF) design T of resolution V is obtained by utilizing the algebraic structure of the underlying multidimentional relationship. Also by using of the multidimensional relationship algebra, the trace and the determinant of the covariance matrix of the estimates of effects are derived.