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The only known recursive constructions are an tripling construction by Denniston \\cite{MR535159}and a product construction by Lei \\cite{MR1931492}, both constructs an LKTS($uv$) on the basis of an LKTS($v$).\n  In this paper, we describe an construction of LKTS$(q^n+2)$ from LKTS$(q+2)$, where $q$ is a prime power of the form $6t+1$. We could construct previous unkno"},"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":"1307.3019","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-11T08:53:44Z","cross_cats_sorted":[],"title_canon_sha256":"ec307d7c4bcb6da2057625dc7f7d6873655606bd42aba5d3dceb8102d0da5075","abstract_canon_sha256":"1ef652296471f4556db52eef1525367b4eec2ea10650b34a9ff3b16958559aab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:52.771882Z","signature_b64":"Dzp7xN1pyRmAwZ1toUKp/9CSUQeTHDRn2L03OSS3N8a85SrkVhYZ/OrzMQQZ12hwo64m3PPyZ7MsqxpYWKmFBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"873212c0f0484e174bc1648173f64314ca68ccd3a6d1f3dc9e84f8001be44d4a","last_reissued_at":"2026-05-17T23:53:52.771261Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:52.771261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Large sets of Kirkman triple systems with order $q^n+2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chen Wang, Cong Shi","submitted_at":"2013-07-11T08:53:44Z","abstract_excerpt":"The existence of Large sets of Kirkman Triple Systems (LKTS) is an old problem in combinatorics. 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