Abstract

A sub-area of discrepancy theory that has received much attention in computer science recently, is that of explicit constructions of low-discrepancy point sets for various types of rectangle families in high dimension. This research has led to interesting applications in error-control coding, distributed protocols, Web document filtering, derandomization, and other areas. We give a short survey of this area here. 1 Introduction One major approach in the general area of derandomization is that of explicit or e#cient constructions. This is the problem of giving e#cient deterministic constructions of various discrete structures (e.g., error-correcting codes, hash function families) whose existence has been shown (typically via probabilistic arguments). Our notion of e#ciency throughout will be that of time polynomial in the size of some natural description of such a structure. A particular class of such structures that has received much attention in the last decade, is that of pseudorand...

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