split as you go along:

use strict;
use warnings;

use Data::Dumper;

my @ASAList;

while (<DATA>)
{
    chomp;
    push(@ASAList, split / /);
}

print Dumper(\@ASAList);

__DATA__
27 25 52
1 2 3
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Output:

$VAR1 = [
          '27',
          '25',
          '52',
          '1',
          '2',
          '3'
        ];
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I added a chomp() as well.

You'll still be limited by the memory of your machine, but this will make more efficient use of what you've got.

Might also try pre-extending your array with something like this:

$ASAList[14000000] = 1;
@ASAList = ();
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