A construction method of new D-, A-optimal weighing designs when N≡3 mod 4 and k⩽N−1.

AbstractIn this paper using circular matrices of order m with elements circular matrices of order t, we construct block matrices having 2m diagonal blocks of the form (N−3)It+3Jt and every other element equal to −1, where N=2mt+1 and m, t≡1 mod 2.Then by deleting appropriate rows a number of non-equivalent new D-, A-optimal weighing designs (N,k,s) are constructed for k⩽N−1, N≡3 mod 4, N