Theory of Computing ------------------- Title : Constructing Small-Bias Sets from Algebraic-Geometric Codes Authors : Avraham Ben-Aroya and Amnon Ta-Shma Volume : 9 Number : 5 Pages : 253-272 URL : https://theoryofcomputing.org/articles/v009a005 Abstract -------- We give an explicit construction of an $\epsilon$-biased set over $k$ bits of size $O(k/(\epsilon^2 \log(1/\epsilon))^{5/4}$. This improves upon previous explicit constructions when $\epsilon$ is roughly (ignoring logarithmic factors) in the range $[k^{-1.5},k^{-0.5}]$. The construction builds on an algebraic geometric code. However, unlike previous constructions, we use low-degree divisors whose degree is significantly smaller than the genus. A preliminary version of this paper appeared in FOCS 2009.