I guess you can create a function such as this: 

    minimax[table_] := Module[{slices},
      slices = table[[All, All, #]] & /@ Range[Last@Dimensions@table];
      Min@Max@slices[[#]] & /@ Range[Last@Dimensions@table]
      ]
Then just run the 

`minimax[t]` where `t` where `t` is your table.