‘D-optimum and quasi-D-optimum second-order designs on a cube’

Abstract

I should like to point out the error in construction of minimal second-order symmetric set I44–2 and absolutely minimal design ξ 4 in my paper. The proper set I44–1 may be constructed as a combination of four half-replicates of the 2 4 factorials with the defining relations, x2x3x4 = I , x1x3x4 = I , x1x2x4 = I and x1x2x3 = I correspondingly for the subset B4 and of four duplicated half-replicates of the 2 3 factorials with the same but negative defining relations for the subsets B4–1 ( i ); the number of different points in B4 is 15 and in I4 , 4–l is 31, although the number of trials is 64, against corresponding numbers 36 and 40 in Table 1 of the paper. For the construction of absolutely minimal design ξ 4 we need to take some modification of set I44–1 with 34 points and we obtain in the same way as in the paper a D -optimum design ξ 4 with the number of points 37 instead of 45 presented in Table 2.