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We prove the existence of such a $B$ of size $|B|\\ge (q-1)/|A/A|$ and show that this bound is in general optimal.\n  The case that $q=p$ is a prime and $A=\\{1,2,\\ldots,\\lambda\\}$ for some positive integer $\\lambda$ is particularly interesting in view of the construction of limited-magnitude error correcting codes. Here we construct a packing set $B$ of size $|B|\\gg p (\\lambda \\log p)^{-1}$ for any $\\lambda \\le c p^{1/2"},"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":"1611.00529","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-02T10:09:46Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"12aac311b19f518cc217e6b2c9e4d1511fe3e42f68f425b42b5e2184d0bfe757","abstract_canon_sha256":"c213449a6914335800c627daa71b444405485fa270178b455f029a8629494928"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:06.336877Z","signature_b64":"kAm74nxGPM121Lui1VXT/Ca/sAsd++LeJ5+wNsm/IEzQtIEiOcxxLQwZGAnmWJav/tKbmdRlNgonRb1aJl9XAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ee597b186f871415796684a7d846b16097d348b29f051ef354fb5482c1269ca","last_reissued_at":"2026-05-18T00:45:06.336530Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:06.336530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Packing Sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.CO","authors_text":"Arne Winterhof, Ilya D. 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