Values of minors of an infinite family of D-optimal designs and their application to the growth problem

We obtain explicit formulae for the values of the 2v - j minors, j = 0, 1, 2, of D-optimal designs of order 2v = x(2) + y(2), v odd, where the design is constructed using two circulant or type 1 incidence matrices of 2 - {2s( 2) + 2s + 1; s(2), s(2); s ( s - 1)} supplementary difference sets ( sds). This allows us to obtain information on the growth problem for families of matrices with moderate growth. Some of our theoretical formulae imply growt h greater than 2(2s(2) + 2s + 1) but experimentation has not yet supported this result. An open problem remains to establish whether the ( 1, 1) compl etely pivoted ( CP) incidence matrices of 2 - {2s(2) + 2s + 1; s(2), s(2); s (s - 1)} sds which yield D-optimal designs can have growth greater than 2 v.