No need for a detailed explanation. When your website is under construction, tell search engines to come back later. That's where we need 503. Here is the codes:
header( ( $_SERVER['SERVER_PROTOCOL'] == 'HTTP/1.1' ? 'HTTP/1.1' : 'HTTP/1.0' ) . ' 503 Service Unavailable', true, 503 ); header( "Retry-After: 3600" );
3600 is the number of seconds for search engines to come back later.