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We use the subgraph structure of $G$ to construct four sequences of $2$-designs, and we compute their parameters. Letting $k_4$ denote the number of $4$-vertex cliques in $G$, we create $62$ additional sequences of $2$-designs from $G$, and show how to express their paramet"},"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":"1507.01289","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-05T22:39:30Z","cross_cats_sorted":[],"title_canon_sha256":"d0b2a2f24def6c89bb0268b0f77ab438c0a089c16d554af79640396076d6ac87","abstract_canon_sha256":"2d830af7e6eeec4d79117fbb9a9c5d9a192a1f7408cd15b5369486318b7a8857"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:01.780797Z","signature_b64":"FgapKbiVfaTP1rr70OD+l9/oueM6VZr8TT7kQwB5ZHsk3luYJGTop8j4ZQi79zyCxQrgXASsewZGB0+tDvzECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb43fc90763ddc0628806803a9918605c5c82fc44bc7f68a30efa9239bdbb100","last_reissued_at":"2026-05-18T01:30:01.780295Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:01.780295Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Designs from Paley graphs and Peisert graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"James Alexander","submitted_at":"2015-07-05T22:39:30Z","abstract_excerpt":"Fix positive integers $p,q,$ and $r$ so that $p$ is prime, $q=p^r$, and $q\\equiv 1$ (mod $4$). 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