Sylvester, Vincent2019-08-212019-08-212019-08-01http://hdl.handle.net/2097/40100This paper introduces the basic elements of geometric discrepancy theory. After some background we discuss lower bounds for two problems, Schmidt’s theorem giving a lower bound for convex sets and Roth’s orthogonal method for the lower bound of the L₂ discrepancy of axis-parallel rectangles in the unit square. Then we introduce two sets with low worst-case discrepancy, the Van der Corput set for two dimensions and the Halton-Hammersley set for arbitrary dimension.en-US© the author. This Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).http://rightsstatements.org/vocab/InC/1.0/Discrepancy theoryReport