<p>Traditional physical experiments are prone to limitations of high costs, time constraints, and safety concerns. Therefore, in recent years, the emergence of computer experiments has revolutionized the way of thinking by simulating real-world phenomena using computational models. In engineering experiments, the integration of space-filling designs with advanced search algorithms enhances the ability to identify optimal solutions in high-dimensional and computationally expensive problems. Latin Hypercube Designs (LHD), as space-filling designs, are in huge demand for model-based engineering and scientific applications. Few search algorithms are available to obtain LHDs with a flexible set of factors and runs based on a specific criterion. Our approach is developing simple search algorithms that finally lead to series of nearly orthogonal LHDs, sliced LHDs, and orthogonal LHDs with good space-filling properties. Further, R functions have also been developed to generate these designs for reaching out to the experimenters with less coding skills, thereby widening the applicability of the proposed designs.</p>