I had to try your tests with bitmaps. Not as elegant as hashes but a bit faster.

#! /usr/bin/perl -slw
use strict;
use Hash::Util qw[ lock_hash unlock_hash ];
use Benchmark qw[ cmpthese ];

our $ITERS ||= -1;

our @items = qw[ age old years ];
our @tests = ( @items, map{ $_ . 'x' } @items );

our $a=0b00000000000000000000000001;
our $b=0b00000000000000000000000010;
our $c=0b00000000000000000000000100;
our $d=0b00000000000000000000001000;
our $e=0b00000000000000000000010000;
our $f=0b00000000000000000000100000;
our $g=0b00000000000000000001000000;
our $h=0b00000000000000000010000000;
our $i=0b00000000000000000100000000;
our $j=0b00000000000000001000000000;
our $k=0b00000000000000010000000000;
our $l=0b00000000000000100000000000;
our $m=0b00000000000001000000000000;
our $n=0b00000000000010000000000000;
our $o=0b00000000000100000000000000;
our $p=0b00000000001000000000000000;
our $q=0b00000000010000000000000000;
our $r=0b00000000100000000000000000;
our $s=0b00000001000000000000000000;
our $t=0b00000010000000000000000000;
our $u=0b00000100000000000000000000;
our $v=0b00001000000000000000000000;
our $w=0b00010000000000000000000000;
our $x=0b00100000000000000000000000;
our $y=0b01000000000000000000000000;
our $z=0b10000000000000000000000000;

our @myitems= (
$a, $b, $c,
);

our @mytest= ( @myitems, $d, $e, $f);
our $myset= $a | $b | $c;



our %set = map{ $_ => 1 } @items; lock_hash %set;
our $set = $;  . join( $;, @items ) . $;;

cmpthese $ITERS, {
    hash => q[
        my $count;
        exists $set{ $_ } and ++$count for @tests;
        print "hash: $count" if $ITERS == 1;
    ],
    index => q[
        my $count;
        1+index $set, $; . $_ . $; and ++$count for @tests;
        print "index: $count" if $ITERS == 1;
    ],
    bitmap => q[
        my $count;
        $myset & $_ and ++$count for @mytest;
        print "bitmap: $count" if $ITERS == 1;
    ],
};

@items = map{ $_ x 5 } 'a' .. 'z';
@tests = ( @items, map{ $_ . 'x' } @items );

unlock_hash %set;
%set = map{ $_ => 1 } @items; lock_hash %set;
$set = $;  . join( $;, @items ) . $;;

@myitems= (
$a, $b, $c, $d, $e, $f, $g, $h, $i, $j,
$k, $l, $m, $n, $o, $p, $q, $r, $s, $t,
$u, $v, $w, $x, $y, $z,
);

@mytest= ( @myitems, map { 0b0 } @myitems);
$myset= 0b11111111111111111111111111;

cmpthese $ITERS, {
    hash => q[
        my $count;
        exists $set{ $_ } and ++$count for @tests;
        print "hash: $count" if $ITERS == 1;
    ],
    index => q[
        my $count;
        1+index $set, $; . $_ . $; and ++$count for @tests;
        print "index: $count" if $ITERS == 1;
    ],
    bitmap => q[
        my $count;
        $myset & $_ and ++$count for @mytest;
        print "bitmap: $count" if $ITERS == 1;
    ],
};
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Results on my machine:

           Rate  index   hash bitmap
index  210823/s     --   -51%   -57%
hash   432785/s   105%     --   -13%
bitmap 494700/s   135%    14%     --
           Rate  index   hash bitmap
index   20276/s     --   -73%   -81%
hash    75918/s   274%     --   -28%
bitmap 105217/s   419%    39%     --
[download]