Construction of uniform U-designs

- The relationship between the averaged discrepancy and generalized wordtype pattern is established.
- A new algorithm to construct uniform U-designs is proposed.
- The advantage is illustrated by comparing with the threshold-accepting algorithm.

Orthogonal array-based Latin hypercubes, also called U-designs, have popularly been adopted for designing a computer experiment. The relationship between the averaged discrepancy of all U-designs generated from a given orthogonal array and the generalized wordtype pattern of the orthogonal array is established. Motivated by the relationship, we define a weighted wordtype pattern and a minimum weighted aberration criterion to compare orthogonal arrays of the same parameters. U-designs generated from an orthogonal array with less weighted aberration are shown to have low discrepancies on average. Then, an algorithm to construct uniform U-designs is proposed. It begins with a minimum weighted aberration orthogonal array and its advantage is illustrated by comparing with the threshold-accepting algorithm.