@techreport{Thiel2009, author = {Thiel, Christoph}, title = {Constructing lattice bases by means of approximations}, address = {D{\"u}sseldorf}, url = {http://nbn-resolving.de/urn:nbn:de:hbz:due62-opus-6128}, year = {2009}, abstract = {The construction of a basis of a certain lattice of interest is a basic tool in many fields of algorithmic number theory. All too often we can not compute with the original lattices because of irrational numbers involved but have to work with approximations of them. While helpful bounds were shown about the reduction of lattice bases in cite{buchmann94reducing}, here we introduce the notion of a \$(epsilon,delta)\$-constructable basis of a lattice and determine the precision of vectors that is necessary to extend a set to a \$(epsilon,delta)\$-constructable basis.}, language = {en} }