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A $q$-analog of a Steiner system (briefly, a $q$-Steiner system), denoted $S_q[t,k,n]$, is a set $S$ of $k$-dimensional subspaces of $\\F_q^n$ such that each $t$-dimensional subspace of $\\F_q^n$ is contained in exactly one element of $S$. Presently, $q$-Steiner systems are known only for $t=1$, and in the trivial cases $t = k$ and $k = n$. Invthis paper, the first nontrivial $q$-Steiner systems with $t >= 2$ are constructed. Specifically, several nonisomorphic $q$-Steiner systems $S_2[2,3,13]$ are found by requiring t"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1304.1462","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-04-04T18:47:22Z","cross_cats_sorted":[],"title_canon_sha256":"168f0422d8c41c5a77a05c1b6ba3ec0ffae1c09f2134072208bbb5c3afcf2b79","abstract_canon_sha256":"6cf79a6242fb68eb01e920e68e0cf20e0208f54dbd876ab2961f89806478dd92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:22.319555Z","signature_b64":"LLrPakXIyV8BMCY/OFcKW9Ln7lHt7odJdi+0ZfEekWbxZr5uA3HLiOWouLa+qK7ndM9fwfZ93XLH0TzvvurmBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9808023997e38c9b3eda0aeaa55e79424609bc06b59d3780bafb4320e0fb8a15","last_reissued_at":"2026-05-18T03:26:22.318773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:22.318773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of $q$-Analogs of Steiner Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexander Vardy, Alfred Wassermann, Michael Braun, Patric Ostergard, Tuvi Etzion","submitted_at":"2013-04-04T18:47:22Z","abstract_excerpt":"Let $\\F_q^n$ be a vector space of dimension $n$ over the finite field $\\F_q$. 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