Niezen, Joanna2013-12-202013-12-2020132013-12-20http://hdl.handle.net/1828/5102A linear space is a set of points and lines such that any pair of points lie on exactly one line together. This is equivalent to a pairwise balanced design PBD(v, K), where there are v points, lines are regarded as blocks, and K ⊆ Z≥2 denotes the set of allowed block sizes. The dimension of a linear space is the maximum integer d such that any set of d points is contained in a proper subspace. Specifically for K = {3, 4, 5}, we determine which values of v admit PBD(v,K) of dimension at least three for all but a short list of possible exceptions under 50. We also observe that dimension can be reduced via a substitution argument.enpairwise balanced designPBDLatin squareMOLSGDDdimensionlinear spacegame of SetSteiner triple systemSTSSteiner spacesubspaceWilson's constructionThesisAvailable to the World Wide Web