AbstractA symmetric nested orthogonal array, denoted by NOA, is an OA which contains an OA as a subarray, where . Nested orthogonal arrays are useful in designing an experimental setup consisting of two experiments, the expensive one of higher accuracy being nested in a relatively less expensive one of lower accuracy. In this paper, some combinatorial constructions of nested orthogonal arrays are provided. By employing these constructions, the existence spectrum of NOA is completely determined.