@inproceedings{2ed6b87d45234e63ac16625dd12b1cac,
title = "Probabilistic existence of rigid combinatorial structures",
abstract = "We show the existence of rigid combinatorial objects which previously were not known to exist. Specifically, for a wide range of the underlying parameters, we show the existence of non-trivial orthogonal arrays, t-designs, and t-wise permutations. In all cases, the sizes of the objects are optimal up to polynomial overhead. The proof of existence is probabilistic. We show that a randomly chosen such object has the required properties with positive yet tiny probability. The main technical ingredient is a special local central limit theorem for suitable lattice random walks with finitely many steps.",
keywords = "designs, local central limit theorem, orthogonal arrays, permutations, probabilistic method",
author = "Greg Kuperberg and Shachar Lovett and Ron Peled",
year = "2012",
doi = "https://doi.org/10.1145/2213977.2214075",
language = "الإنجليزيّة",
isbn = "9781450312455",
series = "Proceedings of the Annual ACM Symposium on Theory of Computing",
pages = "1091--1105",
booktitle = "STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing",
note = "44th Annual ACM Symposium on Theory of Computing, STOC '12 ; Conference date: 19-05-2012 Through 22-05-2012",
}