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2011

Explicit combinatorial design

Ma, Xiongfeng, Zhang, Zhen, Tan, Xiaoqing

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Understand

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 a limited parameter regime.

Explicit combinatorial design · Around

Built on

N. Nisan and A. Wigderson, J. Comput. Syst. Sci., 49
1994
Earlier work this paper cites.
L. Trevisan, Journal of the ACM, 48
1999
Earlier work this paper cites.

Similar

R. Raz, O. Reingold, and S. Vadhan, Journal of Computer and System Sciences, 65
2002
Cited alongside, same era.
T. Hartman and R. Raz, Random Structures & Algorithms, 23
2003
Cited alongside, same era.

Then

In the original definition of weak design, ( n − 1 ) ρ (n-1)\rho instead of n ρ n\rho is used on the right side of Eq. ( 7
2003
Later among the works it cites.
V. Leont’ev, Mathematical Notes, 80
Original
2006
Later among the works it cites.

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