The exponent of discrepancy is at most 1.4778...

We study discrepancy with arbitrary weights in the L₂ norm over the d-dimensional unit cube. The exponent p* of discrepancy is defined as the smallest p for which there exists a positive number K such that for all d and all ε ≤ 1 there exist K^ε-p points with discrepancy at most ε. It is well known that p* ∈ (1, 2]. We improve the upper bound by showing that p* ≤ 1.4778842. This is done by using; relations between discrepancy and integration in the average case setting with the Wiener sheet measure. Our proof is not constructive. The known constructive bound on the exponent p* is 2.454.