Existence and Construction of Orthogonal and Nearly Orthogonal Latin Hypercube Designs with Eight Columns - Singh, Poonam; Kumar, Nilesh (Mathematics and Computer Science: Research Updates Vol. 1, 2025)
Latin hypercube designs are widely used in computer experiments to study complex processes. Orthogonality and space-filling are important criteria used to select good Latin hypercube designs. Orthogonality allows to study of the main effect of each factor independently when a regression model is fitted. Designs with better space-filling properties are used to estimate the meta-model more efficiently. In this chapter, we have solved the problem of the existence and construction of orthogonal Latin hypercube designs (OLHD) with eight columns. In particular, the proposed method is used to construct OLHDs (whenever exist) with eight factors for n = 8k + s runs, where k \(\ge\) 1 is an odd integer and 0 \(\le\) s \(\le\) 7. In addition, nearly orthogonal Latin hypercube designs have been constructed for some values of n for which OLHD (n,8) do not exist. We have also shown that an OLHD (2ut, u) and an OLHD (2ut + 1, u) can always be constructed for u = 8, 16, 32, 64, 96, 128, 160, 192, if a Hadamard matrix of order 4t exists, where t>1 is an integer. All the designs constructed in this chapter can be optimized in terms of discrepancy measures.