Static retrieval with non-power-of-two value domains

Determine whether it is possible to construct a static retrieval data structure for n keys from universe [U] with values drawn from an arbitrary domain [V] (with V ≤ poly(n), not necessarily a power of two) that achieves query time t and total space n log V + floor(n · e^{-O(wt / log V)}) bits, thereby matching the upper bounds established for power-of-two value domains.

Background

The paper proves tight lower and upper bounds for static retrieval when values are v-bit (i.e., V is a power of two) and shows a precise redundancy/time trade-off. These results rely on constructions that operate naturally over bit-level representations, including matrix tools that assume integer bit sizes.

Extending these bounds to arbitrary value ranges [V] that are not powers of two would require accommodating non-integer bit representations. The authors note that a stronger version of the matrix construction (Proposition 3 in Dietzfelbinger and Walzer, 2019) would be needed to handle such domains, and that even variants of this question in field-sized V appear as open in prior work.