Eleven Bits Per Pass

You need to sort $n = 10^5$ records by a 32-bit unsigned key. LSD radix sort with a base of $2^b$ makes $\lceil 32/b \rceil$ passes, and each pass costs about $n + 2^b$ operations: $n$ to scatter the records and $2^b$ to clear and prefix-sum the count array. Total work is

$W(b) = \left\lceil \frac{32}{b} \right\rceil \left(n + 2^{b}\right)$

Which of $b = 8$, $b = 11$, $b = 16$, $b = 32$ minimizes $W$?