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In 2010, Polhill \\cite{Polhill} constructed Paley type partial difference sets in abelian groups with those orders. Thus, combining with the constructions of Polhill and the classical Paley construction using non-zero squares of a finite field, we completely answer the f"},"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":"1908.07055","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-08-19T20:29:15Z","cross_cats_sorted":[],"title_canon_sha256":"dc2355b4ae660d3816c497fd090c634ced00a0324f48f58b5785ae9fed60c36b","abstract_canon_sha256":"541fe04cc118345b547b97f13ab9f9539b2033dead37b0e4d6729920e767f1e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:58:30.391242Z","signature_b64":"lW6QZbtT0UD/1Id+gMq30t40vYY7BVA7jNAp/vZ+YlF5YkniEi3RstyxLYx0vd4klHGbPFzx8wBk4gKnWTiRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82fc36ad97b1ee02ddf6910915eb8fbba05f3f236f3734938865251f88daeaf6","last_reissued_at":"2026-07-04T23:58:30.390766Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:58:30.390766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Paley type partial difference sets in abelian groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zeying Wang","submitted_at":"2019-08-19T20:29:15Z","abstract_excerpt":"Partial difference sets with parameters $(v,k,\\lambda,\\mu)=(v, (v-1)/2, (v-5)/4, (v-1)/4)$ are called Paley type partial difference sets. 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