A closely watched patent infringement trial came to an end Thursday with an attorney for Rambus Inc. asking a federal jury to award the technology firm up to $868 million in damages against a South Korean chip manufacturer.

Rambus sued Hynix Semiconductor in 2000, accusing the computer memory chip manufacturer of infringing on patents Rambus filed in the early ’90s. Hynix, however, counters that Rambus’ patents don’t cover Hynix memory chips, and so it shouldn’t be forced to pay the Los Altos-based technology firm any royalties.