Augmented uniform designs

- Give a new strategy to augment number and/or runs under uniformity criterion.
- Show the lower bounds of wrap-around L2-discrepancy for augmented designs.
- Give the construction algorithm of augmented uniform designs.
- Show that the lower bounds are tight in many cases.
- The new designs are more uniform and flexible than foldover(semifoldover) designs.

Foldover and semifoldover techniques are two important ways to augment the number of runs of a design. However, these methods constrain the number of augmented runs to be equal to or half of that of the initial design. Such constraint may be relaxed in practical application. Moreover, some extra factors may be added in the follow-up designs, and one may augment the number of factors. In this paper, the wrap-around L2-discrepancy criterion is considered to augment the number of runs and the number of factors for mixed two- and three-level designs. The corresponding designs are called as the row augmented uniform designs and the column augmented designs, respectively. The lower bounds of the augmented designs are obtained, and a construction algorithm is also given. Some examples show that many augmented designs can reach the corresponding lower bounds. Compared with the foldover designs and semifoldover designs, the augmented uniform designs are more uniform and flexible.