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  "Title": "Construction of p-Rep Designs from Graph and Finite-Field\nStructures",
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  "Description": "Constructs partially replicated (p-rep) designs in which\nevery treatment occurs in every location, once or twice in\nMethods I and III and q or q + 1 times in Method II, with\nconstant overall replication. Method I decomposes the complete\ngraph into Hamiltonian paths, Method II uses cyclic blocks\nderived from a Hamiltonian cycle, and Method III uses mutually\northogonal Latin squares over a Galois field. Three\ntreatment-replacement extensions (block enlargement, block\nsplitting, and replacement followed by column-wise splitting)\ncan be applied to Methods I and II. Each design is checked for\nconnectedness and is returned with its parameters, pairwise\nconcurrence distribution, canonical efficiency factor (CEF),\naverage variance factor (AVF) and a randomized layout.\nBackground references: Vinaykumar et al. (2026)\n<doi:10.1007/s12355-025-01684-1>; Vinaykumar et al. (2024)\n<doi:10.1080/03610926.2023.2185753>; Williams et al. (2011)\n<doi:10.1002/bimj.201000102>.",
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  "Date/Publication": "2026-11-13 23:10:08 UTC",
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