We previously blogged about Adidas’s successful trademark infringement suit against Collective Brands (owner of Payless Shoes), in which Adidas won a verdict of nearly $305 million, including $137 in punitive damages.

Now Bloomberg.com is reporting that Adidas is pursuing a similar claim against Wal-Mart. Adidas predicts that the punitive damages award against Wal-Mart will exceed the award against Payless, because the jury won’t take kindly to the fact that Wal-Mart repeatedly promised not to mimic Adidas’ designs but did so anyway.

The case against Wal-Mart is pending in the same courthouse where the Payless case was decided. Presumably, if Adidas wins, Oregon will once again come calling for its 60 percent share of the punitive damages.