You can definitely get rid of $count by using push. Here's how I'd do it:

for my $letter ('A'..'H') {
  for my $num (1..12) {
    push(@masterarray, sprintf("$letter%02d", $num));
  }
}
print scalar(@masterarray)," elements\n";
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If you wanted to use some magic, you could do this instead:

for my $letter ('A'..'H') {
    push(@masterarray, $letter.'01'..$letter.'12');
}
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or even

# The golfiest
my @masterarray = map { $_.'01'..$_.'12' } 'A'..'H';
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