IMO the risk is not to have a non reversible key, but to hide
this "a bit". with a small number of output bits there are
not many options.

some approaches

- take a prime number p large then the name space and smaller
than the space to hold the result, take a generator g of the
multiplicative group,  and compute  output = (g ** input) mod p.
for all 1 < input < p
you can iterate this using different primes, add some
"magic" bijectif functions, permutation of bits etc.

- take a fixed secret, and encrypt with des => 8 octets.

-  if your key space is large, 16 octets, you an hmac with
   1 billion times md5 of the input or something like than.

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