This thesis explores and introduces new constructions for non-adaptive group testing which are particulary important for the parameter range... Show moreThis thesis explores and introduces new constructions for non-adaptive group testing which are particulary important for the parameter range we encounter in real life problems. After a summary of existing results, the rst part of this thesis introduces our own constructions, the Latin Square Construction and the Column Augmented Concatenation. Both of these constructions take existing good group testing matrices to create test matrices of larger dimensions. These new matrices are easy to nd for the practical small parameter range we are most interested in. We also address and prove asymptotic results of our Latin Square Construction. In case of the Column Augmented Concatenation the asymptotic results depend greatly on the codes used for the construction. The second part of our work is to address possible ways of augmentation of the Latin Square Construction. Here we explore the di erence in augmentation based on the properties of the starting matrix. In the appendices we give tables of best matrices coming from our constructions with xed, small column weights. We also give a list of the known best 2-disjunct matrices for small row numbers. PH.D in Applied Mathematics, May 2014 Show less
