Deterministic Ω-search for discrete configuration spaces

Many computational workflows are governed by combinations of discrete design decisions. Such systems can be represented by configuration vectors whose components correspond to factor levels drawn from finite sets. Exhaustive exploration of the resulting configuration space rapidly becomes computationally infeasible as the number of factors increases. This paper introduces deterministic 𝛺-search, a structured exploration strategy for discrete configuration spaces based on orthogonal-array sampling. Instead of evaluating all admissible configurations, the method evaluates only a balanced subset defined by a combinatorial experimental design. We formalize the configuration-search problem, derive the induced response algebra under orthogonal-array sampling, and analyze several theoretical properties of the resulting estimators, including orthogonality of factor effects, unbiasedness of level means under balanced projections and bounded optimality under weak interactions. The combinatorial relation between Latin squares and orthogonal arrays is also discussed as a constructive mechanism for generating balanced experimental designs. Several standard designs, including 𝐿₉, 𝐿₁₂, 𝐿₁₆ and 𝐿₂₇, are analyzed in terms of search-budget reduction. Finally, we provide formal guarantees for additive and weakly non-additive response surfaces.