Values of Minors of an Infinite Family of D-Optimal Designs and Their Application to the Growth Problem: II

We obtain explicit formulae for the values of the 2v − j minors, j = 0, 1, 2, of Doptimal designs of order 2v = x2 + y2, v odd, where the design is constructed using two circulant or type 1 incidence matrices of 2−{2s2+2s+1; s2, s2; 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 growth greater than 2(2s2 +2s+1) but experimentation has not yet supported this result. An open problem remains to establish whether the (1,−1) completely pivoted (CP) incidence matrices of 2 − {2s2 + 2s + 1; s2, s2; s(s − 1)} sds which yield D-optimal designs can have growth greater than 2v.