‘ 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 I 4 4–2 and absolutely minimal design ξ 4 in my paper. The proper set I 4 4–1 may be constructed as a combination of four half-replicates of the 2 4 factorials with the defining relations, x 2 x 3 x 4 = I , x 1 x 3 x 4 = I , x 1 x 2 x 4 = I and x 1 x 2 x 3 = I correspondingly for the subset B 4 and of four duplicated half-replicates of the 2 3 factorials with the same but negative defining relations for the subsets B 4–1 ( i ); the number of different points in B 4 is 15 and in I 4 , 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 I 4 4–1 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.