I'm finding is there any range summable hash function.
ADD: The hash function I refer to is the one that is typically used in tug-of-war sketch(AMS sketch). Please refer to The space complexity of approximating the frequency moments.
Improved range-summable random variable construction algorithms gives one for any k-wise independence, but its author Martin J. Strauss shows it is incorrect from his homepage.
The only one I can find is from One-Pass Wavelet Decompositions of Data Streams, where a 4-wise one is given. It used second-order Reed-Muller hash functions.
Are there any other range summable hash functions with 4 or more independence?