This paper presents new infinite families of orthogonal designs for computer experiments. In cases where orthogonal designs cannot exist, we construct alternative, nearly orthogonal designs. Our designs can accommodate many factors and a large set of levels. No iterative computer search is required. To build up the desired orthogonal designs we develop and use new infinite classes of periodic Golay pairs.

Jones and Nachtsheim (2011) propose a new class of computer-generated three-level screening designs called definitive screening designs (DSDs). These designs provide estimates of main effects that are unbiased by any second-order effect and require only one more than twice the number of factors. Stylianou (2011) and Xiao et al. (2012 Xiao, L. , Lin, D. K. J. and Bai, F. 2012. Constructing definitive screening designs using conference matrices. J. Quality Technol., 44: 2–8. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] ) suggest the construction of these designs using conference matrices. The resulting DSD is always global optimum. This method is only applicable when the number of factors is even. This article introduces an algorithm for constructing DSDs for both even and odd numbers of factors using cyclic generators. We show that our algorithm can construct designs that are more efficient than those of Jones and Nachtsheim (2011 Jones, B. and Nachtsheim, C. J. 2011. A class of three levels designs for definitive screening in the presence of second order effects. J. Quality Technolo., 43: 1–15. [Taylor & Francis Online], [Web of Science ®] [Google Scholar] )and that it can construct much larger designs.