Abstract
A Mellon design of order h(2) is a symmetric (4h(2), 2h(2) - h, h(2) - h)-design. Quasi-residual and quasi-derived designs of a Mellon design have parameters 2 - (2h(2) + h, h(2), h(2) - h) and 2 - (2h(2) - h, h(2) - h, h(2) - h - 1), respectively. In this article, regular Hadamard matrices are used to construct non-embeddable quasi-residual and quasi-derived Menon designs. As applications, we construct the first two new infinite families of non-embeddable quasi-residual and quasi-derived Menon designs. (C) 2008 Wiley Periodicals, Inc. J Combin Designs 17: 53-62, 2009