Abstract

We give an explicit construction of a large subset $${S \subset \mathbb{F}^n}$$ S ? F n , where $${\mathbb{F}}$$ F is a finite field, that has small intersection with any affine variety of fixed dimension and bounded degree. Our construction generalizes a recent result of Dvir and Lovett (STOC 2012) who considered varieties of degree one (that is, affine subspaces).

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