Largest VSAM file size, that can be handled by z/OS: For standard VSAM data sets under z/OS, the maximum data set size is four gigabytes, as is documented in the z/OS DFSMS: Using Data Sets manual.
You can also use SMS data classes to create larger VSAM data sets through the use of extended addressability via the extended addressability parameter on screen two of the DATA CLASS DEFINE screen as documented in z/OS DFSMS: Implementing System Managed Storage manual and the z/OS DFSMSdfp Storage Administration Reference manual. There is a limit of 59 volumes to a data class.
When you specify extended format, you can also select requirements for the data set, including the need for extended addressability.
See z/OS DFSMS: Using Data Sets for detailed information on assigning and allocating data classes for extended format data sets.
The EXT Parameter specifies that the data set to be allocated is in the extended format. All VSAM data set types can be allocated in the extended format (with the exception of key range data sets, temporary data sets, and system data sets, including all catalogs).