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### Typical sequence lengths are 10-50k letters
my $sub = "CGAGCGTTGACGCNNAGCTAGT";
...
    ('T') x $bases{t},
    ('N') x $bases{n},
);

my $sub = "CGAGCGTTGACGCNNAGCTAGT";
my @bases = split //, $sub;

   my $sub = 'CGAGCGTTGACGCNNAGCTAGT';
   my @bases = split //, $sub;
...
         $permutations_totals += scalar($string =~ m/$regex/g);
      }
   }

With count == 100:
Benchmark: running mine, yours, each for at least 10 CPU seconds...
...
        Rate yours  mine
yours 7.68/s    --  -57%
mine  17.8/s  132%    --

With count == 100:
Benchmark: running mine, yours, each for at least 10 CPU seconds...
...
        Rate yours  mine
yours 7.55/s    --  -57%
mine  17.4/s  131%    --