Abstract: The construction of a 3-(v, k, lambda) design for given integers v,
k, lambda, is a very important problem in design theory. One can, by
elementary counting arguments, obtain certain arithmetic divisibility
conditions that the parameters have to satisfy, which are by no means
sufficient. It is however conjectured that if v is "sufficiently" large
and the arithmetic conditions are satisfied then there exists a 3-(v,k,lambda)
design. In this dissertation, we look at three different facets of this
problem and construct infinite families of 3-designs by extending known
techniques for construction of 3-designs, and also provide the framework
for a lambda-large problem.