You wanted tweaks :) This is at least smaller.

#!/usr/bin/perl -l

# http://perlmonks.org/?node_id=1188292

use strict;
use warnings;

my $n = shift // 3;  # alphabet size
my $t = shift // $n; # size of tuples

my @alphabet = ('A'..'Z', '0'..'9', 'a'..'z');
my (%next, %all);
@next{'', @alphabet} = @alphabet;

$_ = $alphabet[0] x $t; # start of string
my $over = $alphabet[$n]; # outside of alphabet
my $need = $n ** $t + $t - 1;

1 while s/^(?=(.{$t})) (?=.+\1) (.) | $over(.)/$next{$+}/x # advance c
+har
  or s/^ (?=.{$t}) (?!.{$need}) /$alphabet[0]/x; # add new char

print;         # then prove it is correct
$all{$1}++ while /(?=(.{$t}))/g;
print "want @{[ $n ** $t ]} unique tuples, have @{[ scalar keys %all ]
+}";
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