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- W1898251322 abstract "A combinatorial design is a family of sets that are almost disjoint, which is applied in pseudo random number generations and randomness extractions. The parameter, $rho$, quantifying the overlap between the sets within the family, is directly related to the length of a random seed needed and the efficiency of an extractor. Nisan and Wigderson proposed an explicit construction of designs in 1994. Later in 2003, Hartman and Raz proved a bound of $rhole e^2$ for the Nisan-Wigderson construction in a limited parameter regime. In this work, we prove a tighter bound of $rho<e$ with the entire parameter range by slightly refining the Nisan-Wigderson construction. Following the block idea used by Raz, Reingold, and Vadhan, we present an explicit weak design with $rho=1$." @default.
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- W1898251322 date "2011-09-28" @default.
- W1898251322 modified "2023-09-25" @default.
- W1898251322 title "Explicit combinatorial design" @default.
- W1898251322 doi "https://doi.org/10.48550/arxiv.1109.6147" @default.
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