The encoder always generates the same number of on bits, so same sparsity. For example, a simple encoder using only three primes: 2, 3, 5, would have 10 total bits (2+3+5) with three active bits at all times. It would also be able to encode 30 unique values (2*3*5) before repeating itself. The first few integers would be:
0: 10 100 10000
1: 01 010 01000
2: 10 001 00100
3: 01 100 00010
4: 10 010 00001
5: 01 001 10000
Here, the spaces have been added for clarity to illustrate the individual modulus modules (i.e. N%2 N%3 N%5). Please see the linked thread for additional details.