# Pairwise Balanced Designs with Prescribed Minimum Dimension

Discrete & Computational Geometry, Dec 2013

The dimension of a linear space is the maximum positive integer d such that any d of its points generate a proper subspace. For a set K of integers at least two, recall that a pairwise balanced design $$\operatorname{PBD}(v,K)$$ is a linear space on v points whose lines (or blocks) have sizes belonging to K. We show that, for any prescribed set of sizes K and lower bound d on the dimension, there exists a $$\operatorname{PBD}(v,K)$$ of dimension at least d for all sufficiently large and numerically admissible v.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs00454-013-9564-3.pdf

Peter J. Dukes, Alan C. H. Ling. Pairwise Balanced Designs with Prescribed Minimum Dimension, Discrete & Computational Geometry, 2013, 485-494, DOI: 10.1007/s00454-013-9564-3