limit selectable checkboxes in an array, (max 1 per column, 10 per row, 15 total) based on three php variables

I have an array of checkboxes generated with php. I can not display every checkbox because of previous choices by other users.

for($i=0;$i<$maxrows;$i++)
{
   $already_selected[$i]=0; 
   for($a=0;$a<$maxcols;$a++)
   {
      $value=$mat[$i][$a];
      if($value>0)
      {
         echo"<input type='checkbox' name='arr[$i][$a]' value='$uid'/>";
      }  
      else
      {
         echo"<input type='hidden' name='arr[$i][$a]' value='$value'/>";
         $already_selected[$i]+=1; 
      }
   }   
}

I have to limit the selectable checkboxes in a (for me, at least) complex way: The user must be able to choose: - One checkbox for each column maximum - Maximum $x checkboxes per row (where x is calculated by php as: $maximum_per_row - $already_selected) - Maximum $y checkboxes over the entire grid (where y is a php variable received by the previous page).

Is it possible?

Maybe something like:

echo"
      <script type='text/javascript'>
          var limit = $y;
          $('input.ggrid').on('change', function(evt)
          {
            if($('input[class='ggrid']:checked').length >= limit)
            {
              this.checked = false;
            }
          });
      </script>
";
for($i=0;$i<$maxrows;$i++)
{
   echo"
      <script type='text/javascript'>
          var limit = $maximum_per_row[$i] - $already_selected[$i];
          $('input.row$i').on('change', function(evt)
          {
            if($('input[class='row$i']:checked').length >= limit)
            {
              this.checked = false;
            }
          });
      </script>
   "; 
   for($a=0;$a<$maxcols;$a++)
   {
      echo"
      <script type='text/javascript'>
          var limit = 1;
          $('input.col$a').on('change', function(evt)
          {
            if($('input[class='col$a']:checked').length >= limit)
            {
              this.checked = false;
            }
          });
      </script>
      ";
   }   
}
for($i=0;$i<$maxrows;$i++)
{
   $already_selected=0; 
   for($a=0;$a<$maxcols;$a++)
   {
      $value=$mat[$i][$a];
      if($value>0)
      {
         echo"<input type='checkbox' class='col$a row$i ggrid'name='arr[$i][$a]' value='$uid'/>";
      }  
      else
      {
         echo"<input type='hidden' name='arr[$i][$a]' value='$value'/>";
         $already_selected+=1; 
      }
   }   
}

which obviously does not work... Thank you in advance!