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The construction occurs in any group of order $p^{2}(p+1)$ ($p$ is an odd prime) having ($\\mathbb{F}_{p^{2}},+)$ as an additive subgroup. This construction yields several infinite families of almost difference sets, many of which occur in nonabelian groups. The second construction yields $(4p,2p+1,p,p-1)$ almost differenc"},"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":"1709.07586","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-22T03:38:59Z","cross_cats_sorted":[],"title_canon_sha256":"5c9dc0dd5b02a8501fba1f6324a706d1bb3ac7da9fd528ad98324a812b11dc0f","abstract_canon_sha256":"44f40a4a8a0adf2eac80473125ae8e7e69a42015545d6a67a767c3b980e92baf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:47.714956Z","signature_b64":"TZ87L9BVXMe8Cg4iPSY+SddhIkrv4lc1npgrdxjAC/C8MqzoYxdffRVclQqgWvCmWwnbV+ywPyzBk18Ue1q/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0dae419d860a711fb6e6b305c3b4272ee95d73b5bead1a9af9ba9e544bdc955","last_reissued_at":"2026-05-18T00:09:47.714373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:47.714373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost Difference Sets in Nonabelian Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jerod Michel, Qi Wang","submitted_at":"2017-09-22T03:38:59Z","abstract_excerpt":"We give two new constructions of almost difference sets. 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