If you can't limit yourself to 16 characters, a hash can be used. 
my $lookup = '';
while( <SMALLFILE> ) {
    chomp;
    $lookup{$_} = 1;
}

while( <BIGFILE> ) {
    chomp;
    print if $lookup{$_};
}

[download]

You could pack them smaller if memory is a concern 

my %acgt = (
   A => '00',
   C => '01',
   G => '10',
   T => '11',
);

sub encode {
    my $string = uc shift;
    (my $bin = $string) =~ s/(.)/$acgt{$1}/g
    return pack 'B*', $bin;
}

my $lookup = '';
while( <SMALLFILE> ) {
    chomp;
    $lookup{encode($_)} = 1;
}

while( <BIGFILE> ) {
    chomp;
    print if $lookup{encode($_)};
}

[download]

As is, both my code and yours rely on all strings being the same length, but that's easily "fixed".

In reply to Re^2: Comparing strings (exact matches) in LARGE numbers FAST by ikegami
in thread Comparing strings (exact matches) in LARGE numbers FAST by perlSD

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