Samsung and Apple just can't stay away from the courthouse, and the two tech giants are now back in the ring over Samsung's $1.05 billion fine.

The $1.05 billion marks one of the highest awards ever given in a patent case, but Apple is still not satisfied. While Samsung hopes to overturn the patent verdict or at least reduce the sum, Apple is looking to add at least another half-billion dollars to that amount, and also get a couple of dozen older Samsung products banned in the United States.

The high-profile trial between the two tech giants took place back in August, and saw Apple win significant damages from Samsung, as the South Korean company was found to infringe the iPhone maker's patents.

Samsung is not only arguing that many of Apple's patents should have never been awarded to begin with, but also that the damages award was not correctly calculated, and the jury foreman was biased.

Samsung, obviously uneasy with the California court's decision, is seeking to have the verdict overturned, arguing that the jury foreman acted with "deliberate dishonesty" during jury selection.

The South Korean company is claiming that Velvin Hogan "deliberately concealed information" about a lawsuit he had been involved in two decades ago. That lawsuit was against Seagate, of which Samsung owns 10 percent, and was allegedly the reason Hogan filed for bankruptcy.

"Mr. Hogan's failure to disclose the Seagate suit raises issues of bias that Samsung should have been allowed to explore in questioning," Samsung argued in an October filing to the court.

Consequently, Samsung will ask the court to reduce the amount of damages, and the company can further continue to argue its case in the U.S. appellate courts. Meanwhile, Apple is asking the court to increase the amount in damages, claiming that Samsung should pay even more for allegedly "willful" infringement.

Moreover, Apple is also asking the court to ban some of Samsung's smartphones, including the latest Galaxy S3 flagship handset. The hearing on Thursday, Dec. 6, is also expected to unravel some details regarding the recent patent settlement between Apple and HTC.

The case will be heard by San Jose District Judge Lucy Koh for now, but Samsung is expected to take the case to the federal Circuit Court of Appeals, and possibly even to the Supreme Court.