Lower bounds for centered and wrap-around L 2 -discrepancies and construction of uniform designs by threshold accepting

摘要: We study the uniformity of two- and three-level U-type designs based on centered wrap-around L2-discrepancies. By analyzing known formulae, we find it possible to reexpress them as functions column balance, also Hamming distances rows. These new representations allow obtain two kinds lower bounds, which can be used bench marks in searching uniform designs. An efficient updating procedure for local search heuristic threshold accepting is developed these novel formulations Our implementation this case efficiently generates low discrepancy Their quality assessed using available bounds.