small vps mysql optimization cannot minimize query cache prunes

I have a small vps with 768MB ram. No matter how much I increase query cache size I cannot minimize Query cache prunes per day and furthermore it continuously recommends to increase the table cache as well. Almost all tables in database are InnoDB.

I would really appreciate any suggestion to resolve this problem. I have tried many different my.cnf configurations but I keep having the same problem.

The output of mysqltuner is shown below

Code:

-------- General Statistics --------------------------------------------------
[--] Skipped version check for MySQLTuner script
[OK] Currently running supported MySQL version 5.1.62-cll
[OK] Operating on 32-bit architecture with less than 2GB RAM

-------- Storage Engine Statistics -------------------------------------------
[--] Status: +Archive -BDB -Federated +InnoDB -ISAM -NDBCluster
[--] Data in MyISAM tables: 7M (Tables: 1)
[--] Data in InnoDB tables: 178M (Tables: 341)
[--] Data in MEMORY tables: 0B (Tables: 1)
[!!] Total fragmented tables: 46

-------- Security Recommendations  -------------------------------------------
[OK] All database users have passwords assigned

-------- Performance Metrics -------------------------------------------------
[--] Up for: 8d 9h 37m 44s (65M q [90.854 qps], 196K conn, TX: 100B, RX: 20B)
[--] Reads / Writes: 87% / 13%
[--] Total buffers: 538.0M global + 7.2M per thread (100 max threads)
[!!] Maximum possible memory usage: 1.2G (167% of installed RAM)
[OK] Slow queries: 0% (1K/65M)
[OK] Highest usage of available connections: 79% (79/100)
[OK] Key buffer size / total MyISAM indexes: 16.0M/1.4M
[OK] Key buffer hit rate: 99.9% (3M cached / 2K reads)
[OK] Query cache efficiency: 92.5% (59M cached / 64M selects)
[!!] Query cache prunes per day: 368690
[OK] Sorts requiring temporary tables: 0% (8 temp sorts / 981K sorts)
[OK] Temporary tables created on disk: 10% (159K on disk / 1M total)
[OK] Thread cache hit rate: 99% (79 created / 196K connections)
[!!] Table cache hit rate: 15% (1K open / 6K opened)
[OK] Open file limit used: 0% (13/3K)
[OK] Table locks acquired immediately: 99% (12M immediate / 12M locks)
[OK] InnoDB data size / buffer pool: 178.3M/196.0M

-------- Recommendations -----------------------------------------------------
General recommendations:
    Run OPTIMIZE TABLE to defragment tables for better performance
    Reduce your overall MySQL memory footprint for system stability
    Increasing the query_cache size over 128M may reduce performance
    Increase table_cache gradually to avoid file descriptor limits
Variables to adjust:
  *** MySQL's maximum memory usage is dangerously high ***
  *** Add RAM before increasing MySQL buffer variables ***
    query_cache_size (> 196M) [see warning above]
    table_cache (> 1024)

The settings in my.cnf are shown below

Code:

max_connections=100
query_cache_size=128M
query_cache_limit = 148M
wait_timeout = 10
interactive_timeout = 50
table_cache = 1K
table_definition_cache = 4K
open_files_limit = 3K
innodb open files = 3K
long_query_time = 5
max_connections=90
innodb_buffer_pool_size = 196M
key_buffer_size=16M
key_buffer=16M
tmp_table_size=128M
max_heap_table_size = 128M

I had previously set in my.cnf increased values for query cache size = 196M and table_cache = 2048 but I still had the same problem.

Finally, I always get the recommendation to run optimize tables because my tables are fragmented but since they are InnoDB no matter how many times I run optimize tables I still have fragmented tables.