An explicit combinatorial design

Mathematics – Combinatorics

Scientific paper

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Scientific paper

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 $\rho\le e^2$ for the Nisan-Wigderson construction. In this work, we prove a tighter bound of $\rho

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