An infinite family of non-embeddable Hadamard designs (Q1289364)

A very elegant and simple recursive construction of \(2\)-\((2\lambda+2, \lambda+1, \lambda)\) designs that are not embeddable as residual designs into symmetric Hadamard \(2\)-\((4\lambda+ 3, 2\lambda+1, \lambda)\) designs is described. As an application, an infinite class of non-embeddable designs with \(\lambda= 3(2^m)-1\), \(m\geq 1\), is constructed.