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An operational method to construct UMEBs containing $d(d^{\\prime}-1)$ maximally entangled vectors is established, and two UMEBs in \\(\\mathbb {C}^{5}\\otimes \\mathbb {C}^{6}\\) and \\(\\mathbb {C}^{5}\\otimes \\mathbb {C}^{12}\\) are given as examples. Furthermore, a systematic way of constructing UMEBs containing $d(d^{\\prime}-r)$ maximally entangled vectors in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\) is presented for $r=1,2,\\cdots, d-1$. Correspondingly, two UMEBs in \\(","authors_text":"Gui-Jun Zhang, Shao-Ming Fei, Xin-Lei Yong, Yi-Fan Han, Yuan-hong Tao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-02-21T14:51:32Z","title":"Constructions of Unextendible Maximally Entangled Bases in \\(\\mathbb {C}^{d}\\otimes \\mathbb {C}^{d^{\\prime}}\\)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.07594","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0675fb8309501ec5715937c1b70bb4168e73e3fc185b1bc255242673d43f144c","target":"record","created_at":"2026-05-18T00:22:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"b757d7298bfeb3f2665b76b3ec4d5480836aa5b87af0d00bd47a7a4bd053565d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-02-21T14:51:32Z","title_canon_sha256":"178e1b0b96540728d504670e4b5d6f79c18b50b73645ab73af1824f55883f659"},"schema_version":"1.0","source":{"id":"1802.07594","kind":"arxiv","version":1}},"canonical_sha256":"3b02a9f1902e77607cd0cd79cdb6337a420365328ad282742e0091ab8bfbc3a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b02a9f1902e77607cd0cd79cdb6337a420365328ad282742e0091ab8bfbc3a2","first_computed_at":"2026-05-18T00:22:49.844927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:49.844927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tkxs6YMx2PozFBF11MhiyRqSpSd4fLGWHOHUwdUaMnu8mkB48V/xcwXj00cj/xPeGgxH3yWUl9+8FpodcQUADQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:49.845331Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.07594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0675fb8309501ec5715937c1b70bb4168e73e3fc185b1bc255242673d43f144c","sha256:9db13538e7f9ec683624d1d3f8938426a511a6ddc25e36f4ea1eba76f1673b9a"],"state_sha256":"561da38a0e095d4ba326d655ef1343db1a890d055f87434772e52d171d210290"}