@article{fad34a5d520b4faa85126ae6696afb73,
title = "Set-codes with small intersections and small discrepancies",
abstract = "We address the new problem of designing large families of subsets of a common labeled ground set that simultaneously have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the subsets is less than or equal to one. Our results include an upper bound on the size of such families, and constructions based on transversal designs, packings, and new forms of Latin rectangles. The constructions jointly optimize the size of the family of sets and the labeling scheme and achieve optimal family sizes for many parameter choices. Probabilistic arguments akin to those used for pseudorandom generators lead to significantly suboptimal results when compared to the proposed combinatorial methods. The intersecting sets discrepancy problem is motivated by emerging applications in coding for molecular data storage.",
keywords = "Block designs, Native DNA-based data storage, Set discrepancy",
author = "R. Gabrys and Dau, {H. S.} and Colbourn, {C. J.} and O. Milenkovic",
note = "Funding Information: \ast Received by the editors January 28, 2019; accepted for publication (in revised form) December 4, 2019; published electronically May 18, 2020. Part of the results in the paper were presented at the IEEE International Symposium on Information Theory, Paris, France, July 2019 [12]. https://doi.org/10.1137/19M1241106 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work was supported in part by NSF grants CCF 1526875, 1816913, and 1813729, and by the DARPA Molecular Informatics Program. \dagger Coordinated Science Laboratory (CSL), University of Illinois at Urbana-Champaign (UIUC), Urbana, IL 61801 (ryan.gabrys@gmail.com, milenkov@illinois.edu). \ddagger Monash University, Melbourne, Australia (hoang.dau@monash.edu). \S Arizona State University, Tempe, AZ 85287-8809 (colbourn@asu.edu). Publisher Copyright: Copyright {\textcopyright} by SIAM. Unauthorized reproduction of this article is prohibited.",
year = "2020",
doi = "10.1137/19M1241106",
language = "English (US)",
volume = "34",
pages = "1148--1171",
journal = "SIAM Journal on Discrete Mathematics",
issn = "0895-4801",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}