On the construction of n-dimensional designs from 2-dimensional designs

design, then = (f(hI + h2 + ... + hn») is a proper n-dimensional design. A difficulty with this construction that it can applied to small number of (2dimensional) designs. This paper develm)s a very general technique for generating a proper n -dimensional design from 2-dimensional designs. Indeed, it is shown that Drake's generalised Hadamard matrices, Berman's nega-cyclic and (i)-cyclic (generalised) weighing matrices b oth of the orthogonal designs of order 4 and type (1,1,1,1) can be extended to proper n-dim ensional In