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We generalize the method to construct MUMEB's given in [16], by using any commutative ring $R$ with $d$ elements and generic character of $(R,+)$ instead of $\\mathbb{Z}_d=\\mathbb{Z}/d\\mathbb{Z}$. Particularly, if $d=p_1^{a_1}p_2^{a_2}\\ldots p_s^{a_s}$ where $p_1, \\ldots, p_s$ are distinct primes and $3\\leq p_1^{a_1}\\leq\\cdots\\leq p_s^{a_s}$, we present $p_1^{a_1}-1$ MUMEB's in $\\mathbb{C}^d\\otimes\\mathbb{C}^d$ by taking $R=\\mathbb{F}_{p_1^{a_1}}\\oplus\\cdots\\oplus\\mat","authors_text":"Junying Liu, Keqin Feng, Minghui Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-09T07:37:12Z","title":"Mutually unbiased maximally entangled bases in $\\mathbb{C}^d\\otimes\\mathbb{C}^d$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.02674","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":"sha256:20ddfe39709875357eece44af707f68602cb9c011e478b32f925beb5a08c9fbc","target":"record","created_at":"2026-05-18T01:04:52Z","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":"7c190958cf3ec0bbcef64219432a205b901ffac13d4a1a33ca4b20d1c2c38413","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-09-09T07:37:12Z","title_canon_sha256":"d40a6f6ccc024b8ca15e449a952946134995493090c70c016d0164428414cc32"},"schema_version":"1.0","source":{"id":"1609.02674","kind":"arxiv","version":1}},"canonical_sha256":"ba56a8bc0a3c16fddab3d090ac385b98306df05b99bd7f901e192e10413d13a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba56a8bc0a3c16fddab3d090ac385b98306df05b99bd7f901e192e10413d13a1","first_computed_at":"2026-05-18T01:04:52.785426Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:52.785426Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u0D/wRsii+hNYGBnN9tJXrWB0sPbJMkD4+aLbZ87iRMrdcbYXDeQBuZZrB+KSs14R0Lm1F/LKiw9UAJnyzneAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:52.786015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.02674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20ddfe39709875357eece44af707f68602cb9c011e478b32f925beb5a08c9fbc","sha256:4a544a00810c83730e41c05fbf88ea8125f1e37d4bd4195c0d29dc2b1b06b7c3"],"state_sha256":"301fb96179bb0ef0b79531106bf63437dd7cca5b780d0fb5a03ef35aac8e3169"}