A-Optimal Weighing Designs with n ≡ 3(mod4) and their Information Matrix Form

In cases of constructing weighing (or factorial) designs, the problem of optimality arises. In this paper we study the form of the information matrices of A-Optimal Weighing Designs (n,k,sopt) (abrv. A-OWD), when the number of observations is n≡3(mod4). We are interested in critical values ko(n) for which the next statement is valid: “If k ≥ko(n) then M k * ≠ (n+1)·Ik−Jk, where Ik is the identity matrix of order k and Jk is a k×k matrix with all its entries equal 1”. The symbol (*) on the information matrix Mk means A-optimality.