I tried to get this to you earlier, but I couldn't get the 'push @{$prec}' working because I thought it was an array (not an arrayref. :\ )

This code is along the lines of 'Aren't you really just counting up to a number using base 4?'

use Math::BaseArith;

my $base = 4;

#Start with 2 digits of precision
my $prec = [$base, $base]; 

for my $i (2..3) {
  my $max = ($base ** $i);
  PREC:
  for my $line (0..4**$i) {
    last PREC if ($line >= $max ); #Check for overflow
    print encode( $line, $prec), "\n";
  }
  push @{$prec}, $base; #+Another digit of precision.    
}
[download]

That was kind of fun!

Update: Made numeric comp (>=), and corrected max.

Kurt