Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In polynomial regression modeling, the use of a second order orthogonal Latin hypercube design guarantees that the estimates of the first order effects are uncorrelated to each other as ll as to the estimates of the second order effects. ,  prove that such designs with nn runs and k>2k>2 columns do not exist if n≡4mod8n≡4mod8. Furthermore,  prove that second order Latin hypercube designs with k≥4k≥4 columns that guarantee the orthogonality of two-factor interactions which do not share a common factor, do not exist for even nn that is not a multiple of 16. Finally,  investigate the class of symmetric orthogonal Latin hypercube designs (SOLHD), which are a special subset of second order orthogonal Latin hypercube designs.  describe construction techniques for SOLHDs with nn runs and (a) k≤4k≤4 columns, when n≡0mod8n≡0mod8 or n≡1mod8n≡1mod8, (b) k≤8k≤8 columns when n≡0mod16n≡0mod16 or n≡1mod16n≡1mod16 and (c) k=4k=4 columns when n≡0mod16n≡0mod16 or n≡1mod16n≡1mod16, that guarantee the orthogonality of two-factor interactions which do not share a common factor. Finally,  construct and enumerate all non-isomorphic SOLHDs with n≤17n≤17 runs and k≥2k≥2 columns, as ll as with 19≤n≤2019≤n≤20 runs and k=2k=2 columns.
['Haralambos Evangelaras', 'Markos V. Koutras']
I am writing a research paper on a idea On second order orthogonal Latin hypercube designs
[{"from": "human", "value": "I am writing a research paper on a idea On second order orthogonal Latin hypercube designs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: In polynomial regression modeling, the use of a second order orthogonal Latin hypercube design guarantees that the estimates of the first order effects are uncorrelated to each other as ll as to the estimates of the second order effects. ,  prove that such designs with nn runs and k>2k>2 columns do not exist if n\u22614mod8n\u22614mod8. Furthermore,  prove that second order Latin hypercube designs with k\u22654k\u22654 columns that guarantee the orthogonality of two-factor interactions which do not share a common factor, do not exist for even nn that is not a multiple of 16. Finally,  investigate the class of symmetric orthogonal Latin hypercube designs (SOLHD), which are a special subset of second order orthogonal Latin hypercube designs.  describe construction techniques for SOLHDs with nn runs and (a) k\u22644k\u22644 columns, when n\u22610mod8n\u22610mod8 or n\u22611mod8n\u22611mod8, (b) k\u22648k\u22648 columns when n\u22610mod16n\u22610mod16 or n\u22611mod16n\u22611mod16 and (c) k=4k=4 columns when n\u22610mod16n\u22610mod16 or n\u22611mod16n\u22611mod16, that guarantee the orthogonality of two-factor interactions which do not share a common factor. Finally,  construct and enumerate all non-isomorphic SOLHDs with n\u226417n\u226417 runs and k\u22652k\u22652 columns, as ll as with 19\u2264n\u22642019\u2264n\u226420 runs and k=2k=2 columns."}]