The range operator is .. , not . , so I think you you want 1..3 and 1..10.

Also, in your close PIPE or die, be aware that close on a pipe doesn't always set $!. perldoc -f close gives example:

                close OUTPUT                # wait for sort to finish
                    or warn $! ? "Error closing sort pipe: $!"
                               : "Exit status $? from sort";
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Update: changing both scripts to use .. instead of . and removing the extra stuff before #!/usr/bin/perl in net.pl gives this output:

$ perl -w net1.pl
Writing line 1
 Read_three,got This is line number 1

Writing line 2
 Read_three,got This is line number 2

Writing line 3
 Read_three,got This is line number 3

Writing line 4
 An error occured during writing :Broken pipe at net1.pl line 14.
Wrote 3 lines of text
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which looks to me like what you should be expecting. If you have other expectations, please share them so others can help you further.

Update: also added a -w to net2.pl's shebang line