open (OUTHANDLE, ">$basedir . /output/file.txt") or die ;

You're trying to open a file that doesn't exist.

perl -le 'print ">$basedir . /output/file.txt"'
results . /output/file.txt
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There's no concatenating operator there, you clobber them all in one single string, the $basedir, the dot with spaces ( .), and /output/file.txt. Should you use $! variable, Perl would tell you what was wrong.

my $basedir = "results";
my $filename = "$basedir . /output/file.txt";
open (OUTHANDLE, ">$filename") or die "can't open ($filename): $!\n";
can't open (result . /output/file.txt): No such file or directory
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You actually want,

open (OUTHANDLE, ">$basedir" . "/output/file.txt") or die $!;
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but this is not good although it probably works. Use suggestions from other replies.