For designs of computer experiments, column-orthogonality and space-filling property are two desirable properties. In this paper, we develop methods for constructing a new class of designs that include orthogonal Latin hypercube designs as special cases. These designs are not only column-orthogonal but also have good space-filling properties in low dimensions. All these appealing properties make them good choices for designing computer experiments. Based on orthogonal arrays, the proposed methods are easy to operate and flexible. Many new orthogonal designs with desirable space-filling properties are constructed and tabulated. Rotation matrices play a key role in the construction.