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Our lower bound is tight when d=k-1.\n  The orthogonal array problem includes the following problems as special cases: k-sum problem with d=k-1, k-distinctness problem with d=1, k-pattern problem with d=0, (d-1)-degree problem with 1<=d<=k-1, unordered search with d=0 and k=1, and graph collision with d=0 and k=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":"1304.0845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-04-03T05:36:55Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"02fcfa0a1cffa02cc9dd4a8a1435a1c5c289eaebd0a0339f827ec14ee8657902","abstract_canon_sha256":"a92b0274feb27274f3b012b1ac16330f38542b0cdd1982aeb1946699d6fd6492"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:05.964972Z","signature_b64":"8v3nJ73JDcIRuUJV/+BPlicwJVws3K/79+ROGdjTfhCpwljWrqVyavL7EajWXQJpPhCfvn9Zh30xAVauo8iIBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abf580356f15e859a14214214263d47af88a455db679a5a97348286d6978bde5","last_reissued_at":"2026-05-18T03:29:05.964483Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:05.964483Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Adversary Lower Bound for the Orthogonal Array Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Robert Spalek (Google)","submitted_at":"2013-04-03T05:36:55Z","abstract_excerpt":"We prove a quantum query lower bound \\Omega(n^{(d+1)/(d+2)}) for the problem of deciding whether an input string of size n contains a k-tuple which belongs to a fixed orthogonal array on k factors of strength d<=k-1 and index 1, provided that the alphabet size is sufficiently large. 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