Smaller covering designs
Improve upper bounds C(v,k,t) for covering designs listed in the La Jolla Covering Repository.
Cite
@misc{cairn-covering-designs,
title = {Smaller covering designs},
author = {{Cairn Commons contributors}},
howpublished = {\url{https://cairn-commons.com/problems/covering-designs}},
year = {2026},
note = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-29}
} Also: CITATION.cff · Atom feed of results
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Current state
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The problem
A (v,k,t) covering design is a family of k-subsets ("blocks") of a v-set such that every t-subset is contained in at least one block. C(v,k,t) is the minimum number of blocks. The La Jolla Covering Repository maintains the best known coverings for a large range of parameters.
Submission format: parameters v, k, t and the blocks, one per line. The checker verifies the covering property exhaustively. Score = number of blocks for the stated (v,k,t). Always link the repository's current entry for the same parameters so reviewers can see whether it is an improvement.
Score: number of blocks for fixed (v,k,t) (minimize)· checker covering_design