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    copied!<p>I'd probably use SparseArrays here (<strong>see update below</strong>), but if you insist on using functions and *Values to store and retrieve values an approach would be to have the first part (f[2] etc.) replaced by a symbol you create on the fly like:</p> <pre><code>Table[Symbol["f" &lt;&gt; IntegerString[i, 10, 3]], {i, 11}] (* ==&gt; {f001, f002, f003, f004, f005, f006, f007, f008, f009, f010, f011} *) Symbol["f" &lt;&gt; IntegerString[56, 10, 3]] (* ==&gt; f056 *) Symbol["f" &lt;&gt; IntegerString[56, 10, 3]][{3, 4}] = 12; Symbol["f" &lt;&gt; IntegerString[56, 10, 3]][{23, 18}] = 12; Symbol["f" &lt;&gt; IntegerString[56, 10, 3]] // Evaluate // DownValues (* ==&gt; {HoldPattern[f056[{3, 4}]] :&gt; 12, HoldPattern[f056[{23, 18}]] :&gt; 12} *) f056 // DownValues (* ==&gt; {HoldPattern[f056[{3, 4}]] :&gt; 12, HoldPattern[f056[{23, 18}]] :&gt; 12} *) </code></pre> <p>Personally I prefer Leonid's solution, as it's much more elegant but YMMV.</p> <p><strong>Update</strong></p> <p>On OP's request, about using <code>SparseArrays</code>:<br> Large SparseArrays take up a fraction of the size of standard nested lists. We can make f to be a large (100,000 entires) sparse array of sparse arrays:</p> <pre><code>f = SparseArray[{_} -&gt; 0, 100000]; f // ByteCount (* ==&gt; 672 *) (* initialize f with sparse arrays, takes a few seconds with f this large *) Do[ f[[i]] = SparseArray[{_} -&gt; 0, {100, 110}], {i,100000}] // Timing//First (* ==&gt; 18.923 *) (* this takes about 2.5% of the memory that a normal array would take: *) f // ByteCount (* ==&gt; 108000040 *) ConstantArray[0, {100000, 100, 100}] // ByteCount (* ==&gt; 4000000176 *) (* counting phase *) f[[1]][[1, 2]]++; f[[1]][[1, 2]]++; f[[1]][[42, 64]]++; f[[2]][[100, 11]]++; (* reporting phase *) f[[1]] // ArrayRules f[[2]] // ArrayRules f // ArrayRules (* ==&gt;{{1, 2} -&gt; 2, {42, 64} -&gt; 1, {_, _} -&gt; 0} ==&gt;{{100, 11} -&gt; 1, {_, _} -&gt; 0} ==&gt;{{1, 1, 2} -&gt; 2, {1, 42, 64} -&gt; 1, {2, 100, 11} -&gt; 1, {_, _, _} -&gt; 0} *) </code></pre> <p>As you can see, <code>ArrayRules</code> makes a nice list with contributions and counts. This can be done for each f[i] separately or the whole bunch together (last line).</p>
 

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