A method for constructing generalised residual designs

A t-design rc with parameters t (u, k, A) is a finite incidence structure with u points and k points on each block such that any t-subset is contained in exactly 1 blocks. Incidence between a point P and a block d is denoted by P 1 d or d 1 P. We usually denote by b the number of blocks of 17. A block p of a t-design (t > 1) is said to be repeated x times if there exists exactly x blocks d such that Cp] = [d], w h ere [d] denotes the set of points incident with d. We say that p and d are conjugate blocks and that the repetition number of p is the integer x. A theorem due to Mann [6] states that in a 2 (a, k, 1) design I7 with b blocks, b/u is an upper bound on the repetition number of any block. If this upper bound is achieved for a block c, then we call c a max block of Z7. For basic results and definitions of design theory see Dembowski [3].