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Correction for UPTON and LEE, Biometrika 63 (2) 335-342.
Biometrika 1976 63(2):412; doi:10.1093/biomet/63.2.412-a
© 1976 by Biometrika Trust
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CORRECTIONS AND AMENDMENTS

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

L. L. PESOTCHINSKY

I should like to point out the error in construction of minimal second-order symmetric set I4 4–2 and absolutely minimal design {xi}4 in my paper.

The proper set I4 4–1 may be constructed as a combination of four half-replicates of the 24 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 23 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 {xi}4 we need to take some modification of set I4 4–1 with 34 points and we obtain in the same way as in the paper a D-optimum design {xi}4 with the number of points 37 instead of 45 presented in Table 2.


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