my $check = m/$mystrings[N]/;
[download]

... on incrementing values of N:

#! /usr/bin/perl -w

###############
## Libraries ##
###############
use strict;
use warnings;
use File::Basename;
use B::Deparse;
use IO::File;


#############
## Globals ##
#############
my $iam = basename $0;
$| = 1;

my $b_verbose = 0;

my $text = q{
    use strict;
    use warnings;
    my @mystrings = ( "string" ) x 200;

    my $check = m/$mystrings[<NUM>]/;
};


##################
## Main Program ##
##################
for (my $i = 0; $i <= 1000; $i++) {
    try($i);
}


#################
## Subroutines ##
#################
sub try {
    my ($n) = @_;
    my $new = $text;
    $new =~ s/<NUM>/$n/g;
    my $fn = 'test.pl';
    my $fh = new IO::File($fn, "w") or die "Can't write '$fn' ($!)\n";
    print $fh "$new\n";
    close $fh;
    chomp(my @results = `perl -MO=Deparse $fn 2>&1`);
    my ($check) = grep { /check/ } @results;
    my $b_ok = ($check =~ /my \$check = \$mystrings\[\d+\]/)? 1: 0;
    if ($b_verbose) {
        printf "Value %4d => %s\n", $n, $b_ok? "Okay": "*** FAILS ***"
+;
    } else {
        printf "%s", $b_ok? '.': '@';
    }
}
[download]

It prints '.' or '@' for "Okay" and "Failed" values of N, respectively.

You can also assign $b_verbose to a nonzero value to see more verbose results :)