Running time of LSD Radix sort for sorting N records with w byte keys is proportional to Nw , because algorithms makes w passes over all N keys.
For long keys and short bytes this running time is comparable to $N\lg N$.
Property 1 : The worst case for radix sorting is to examine all the bytes in all keys.
Property 2 : Binary quicksort examines about $N\lg N$ bits, on average, when sorting keys composed of random bits.
Property 3 : MSD radix sort with radix R on a file of size N requires at least $2N+2R$ steps.
Property 4 : If the radix is always less than the file size, the number of steps taken by MSD radix sort is within a small constant factor of $N\log_R N$ on the average ( for keys compromising random bytes ), and within a small constant factor of the number of bytes in the keys in the worst case.
Property 5 : Three-way quicksort uses $2N \lg N$ byte comparisons, on the average, to sort N( arbitrarily long ) keys.
Property 6 : LSD radix sort can sort N records with w-bit keys in $\frac{w}{\lg R}$ passes, using extra space for R counters (and a buffer for rearranging the file).