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Award ID contains: 1814298

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  1. ; (, Journal of Combinatorial Designs)
    Abstract The maximum independence number of Steiner triple systems of order is well‐known. Motivated by questions of access balancing in storage systems, we determine the maximum total cardinality of a pair of disjoint independent sets of Steiner triple systems of order for all admissible orders. 
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  2. (, Discrete Mathematics)
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  3. ; ; ; ; (, 2022 IEEE International Symposium on Information Theory (ISIT))
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  4. (, Designs, Codes and Cryptography)
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  5. (, Graphs and Combinatorics)
    null (Ed.)
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  6. ; ; ; ; ; ; (, Designs, Codes and Cryptography)
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  7. (, 2020 Algebraic and Combinatorial Coding Theory (ACCT))
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  8. ; ; ; ; ; ; (, 2020 IEEE International Symposium on Information Theory (ISIT))
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  9. ; ; ; (, SIAM Journal on Discrete Mathematics)
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  10. ; ; ; (, 2019 IEEE International Symposium on Information Theory (ISIT))
    We are concerned with the problem of designing large families of subsets over a common labeled ground set that have small pairwise intersections and the property that the maximum discrepancy of the label values within each of the sets is less than or equal to one. Our results, based on transversal designs, factorizations of packings and Latin rectangles, show that by jointly constructing the sets and labeling scheme, one can 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 design problem considered is motivated by applications in molecular data storage. 
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