Construction methods for Bhaskar Rao and related designs

Abstract

Mathematical and computational techniques are described for constructing and enumerating generalized Bhaskar Rao designs (GBRD's). In particular, these methods are applied to GBRD(k + l,k,l(k -1); G)'s for / > 1. Properties of the enumerated designs, such as automorphism groups, resolutions and contracted designs, are tabulated. Also described are applications to group divisible designs, multi-dimensional Howell cubes, generalized Room squares, equidistant permutation arrays, and doubly resolvable two-fold triple systems.

Enumeration of generalized Hadamard matrices of order 16 and related designs

“…Note that the numbers of signings of GDD32.3 and GDD32.4 correct those reported in [5]. The generation of GDDs includes all generalized Hadamard matrices of order 16 (see [4], Theorem 2, p. 12). These are recognized by the fact that the automorphism group acts regularly on the point and block groups.…”

Generalized Bhaskar Rao Designs with Block Size 3 over Finite Abelian Groups

“…The restriction has applicability to other groups however. [15,Theorem 2]) Let N be a normal subgroup of G, and suppose a (v, k, λ; G) GBRD exists. Then a (v, k, λ; G/N ) GBRD exists.…”

A Block Negacyclic Bush-Type Hadamard Matrix and Two Strongly Regular Graphs

“…Despite the fact that several method of construction is available for balanced generalized matrices, see, for example, [6,8], not much is known about the existence of symmetric or skew balanced generalized weighing matrices with zero diagonal. Symmetric BGWs with zero diagonal, as we will see, are essential to our construction of SRGs.…”