displaying blocks on certain content types only and front page

i have written the following code to display blocks for a specific content type and it works great
but what i want to do is to modify the code so that the block displays on the front page only AND for the mentioned content type but i cant figure out how to do it

<?php
$match = FALSE;
$types = array('story' => 1);
if (arg(0) == 'node' && is_numeric(arg(1))) {
$nid = arg(1);
$node = node_load(array('nid' => $nid));
$type = $node -> type;
if (isset($types[$type])) {
$match = TRUE;
}
}
return $match;
?>