LNMSHASHTBL sets the size of the system logical name hash table.
    Logical names are hashed using a function of the name length
    and contents. The LNMSHASHTBL parameter determines the number
    of entries for shareable logical names. These names include all
    names from the system, group, and job logical name tables. The
    recommended setting allows one to four logical names per hash
    table entry. The default setting is usually adequate, unless
    your installation has a large number of groups, or many jobs are
    active simultaneously. In that case, an increase in the value of
    the next higher power of 2 might improve logical name translation
    performance. Note that the hashed values are rounded up to the
    nearest power of 2.

    LNMSHASHTBL has the AUTOGEN, FEEDBACK, and GEN attributes.