In this paper we consider experimental situations where a 2-level main effects plan is to be used to study m-factors using n runs which are partitioned into b blocks of size k=n/b and where k is an odd integer. For odd k≥3 and certain cases where b is a multiple of k, we show how to construct...

In this paper we consider experimental situations in which m 2-level factors are to be studied using a main effects plan where n runs are partitioned into b block of size k. For the case n≡3 (mod 4), we establish some sufficient conditions for a design to be E-optimal and then give a method...

U-type designs and orthogonal Latin hypercube designs (OLHDs) have been used extensively for performing computer experiments. Both have good spaced filling properties in one-dimension. U-type designs may not have low correlations among the main effects, quadratic effects and two-factor...

Abstract: Divisible design graphs (DDG for short) have been recently defined by Kharaghani, Meulenberg and the second author as a generalization of (v, k, λ)-graphs. In this paper we give some new constructions of DDGs, most of them using Hadamard matrices and (v, k, λ)-graphs. For three...

Using results on Hadamard difference sets, we construct regular graphical Hadamard matrices of negative type of order 4m4 for every positive integer m. If m 1, such a Hadamard matrix is equivalent to a strongly regular graph with parameters (4m4, 2m4 +m2,m4 +m2,m4 +m2). Strongly regular graphs...

The energy of a graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Koolen and Moulton have proved that the energy of a graph on n vertices is at most n(1 + √n)/2, and that equality holds if and only if the graph is strongly regular with parameters (n,...

Theoretical results are derived for finding D-optimal two-level orthogonal arrays for estimating main effects and some specified two-factor interactions. The upper bounds of the determinant of the related matrix for D-optimality are obtained. For run sizes 12 and 20, D-optimal orthogonal arrays...

In this article, I discuss the main approaches to resampling variance es- timation in complex survey data: balanced repeated replication, the jackknife, and the bootstrap. Balanced repeated replication and the jackknife are implemented in the Stata svy suite. The bootstrap for complex survey...