{"id":"W2080714423","doi":"10.1016/j.disc.2008.06.012","title":"Existence of <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si3.gif\" display=\"inline\" overflow=\"scroll\"><mml:mi>r</mml:mi></mml:math>-fold perfect <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si4.gif\" display=\"inline\" overflow=\"scroll\"><mml:mrow><mml:mo>(</mml:mo><mml:mi>v</mml:mi><mml:mo>,</mml:mo><mml:mi>K</mml:mi><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-Mendelsohn designs with <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" altimg=\"si5.gif\" display=\"inline\" overflow=\"scroll\"><mml:mi>K</mml:mi><mml:mo>⊆</mml:mo><mml:mrow><mml:mo>{</mml:mo><mml:mn>4</mml:mn><mml:mo>,</mml:mo><mml:mn>5</mml:mn><mml:mo>,</mml:mo><mml:mn>6</mml:mn><mml:mo>,</mml:mo><mml:mn>7</mml:mn><mml:mo>}</mml:mo></mml:mrow></mml:math>","year":2008,"lang":"lv","type":"article","venue":"Discrete Mathematics","topic":"graph theory and CDMA systems","field":"Engineering","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"Mount Saint Vincent University","funders":"","keywords":"Combinatorics; Mathematics; Integer (computer science); Block (permutation group theory); Discrete mathematics; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.002243973,0.001390135,0.001323007,0.001361322,0.001823475,0.003874493,0.001005217,0.001760718,0.1076177],"category_scores_gemma":[0.009489907,0.0009805639,0.002163072,0.001026912,0.001969767,0.005383973,0.002139053,0.002331872,0.03873792],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001513149,"about_ca_system_score_gemma":0.001570051,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008542337,"about_ca_topic_score_gemma":0.001594316,"domain_scores_codex":[0.9975472,0.0005112004,0.0002008686,0.000667377,0.0007506151,0.000322786],"domain_scores_gemma":[0.9944537,0.0019886,0.0005882698,0.0009678721,0.00168867,0.0003128401],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000428412,0.0001829237,0.0009399407,0.0007370281,0.0001004311,0.000478595,0.0007574448,0.002387441,0.009442532,0.8349151,0.03684741,0.1127827],"study_design_scores_gemma":[0.0002371799,0.000446657,0.001166559,0.0003747242,0.0001119297,0.001273438,0.0005447057,0.006244546,0.01818877,0.7196905,0.2515729,0.0001481793],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.04066523,0.001456192,0.5571139,0.002674147,0.001280231,0.000266207,0.002240392,0.002581482,0.3917222],"genre_scores_gemma":[0.3831856,0.001724309,0.2895948,0.001871518,0.0007440842,0.0007313134,0.004413224,0.002137689,0.3155974],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.1076177,"threshold_uncertainty_score":0.360017,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02103768154853112,"score_gpt":0.2378014874144261,"score_spread":0.2167638058658949,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}