Values of Minors of Some Infinite Families of Matrices Constructed from Supplementary Difference Sets and Their Application to the Growth Problem

We obtain explicit formulae for the values of the 2v - j minors, j = 0,1, 2 of (1, -1) matrices of order 2v, v odd, where the matrix is constructed using two circulant or type 1 incidence matrices of 2— {v; k1, k2, λ} 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 close to the order 2v but experimentation has not yet supported this result. An open problem remains to establish whether the (1, -1) CP incidence matrices of certain SBIBDs, can have growth greater than 2v.