Some constructions of divisible designs from Laguerre geometries

Class-Uniformly Resolvable Group Divisible Structures I: Resolvable Group Divisible Designs

We consider Class-Uniformly Resolvable Group Divisible Designs (CURGDD), which are resolvable group divisible designs in which each of the resolution classes has the same number of blocks of each size. We derive the fully general necessary conditions including a number of extremal bounds. We present some general constructions including a novel construction for shrinking the index of a master de...

Divisible Designs, Laguerre Geometry, and Beyond

Further results on large sets of disjoint group-divisible designs

Chen, D., CC. Lindner and D.R. Stinson, Further results on large sets of disjoint group-divisible designs, Discrete Mathematics 110 (1992) 35-42. This paper is a continuation of a recent paper by Chen and Stinson, where some recursive constructions for large sets of group-divisible design with block size 3 arc presented. In this paper, we give two new recursive constructions. In particular, we ...

Variations on the McFarland and Spence constructions of difference sets

We give two new constructions of symmetric group divisible designs using divisible difference sets. These constructions generalize the McFarland and Spence constructions of symmetric designs. Divisible designs are of interest in several parts of mathematics: The design theorist needs classes of divisible designs as "ingredients" for recursive constructions of designs. Statisticians use divisibl...

Balanced Arrays of Strength Two from Block Designs

Some constructions of balanced arrays of strength two are provided by use of rectangular designs, group divisible designs, and nested balanced incomplete block designs. Some series of such arrays are also presented as well as orthogonal arrays, with illustrations. # 2002 Wiley Periodicals, Inc. J Combin Designs 10: 303–312, 2002; Published online in Wiley InterScience (www.interscience.wiley.co...