  The Invertible Bloom Lookup Table (IBLT) is a probabilistic data structure
for set representation, with applications in network and traffic monitoring. It
is known for its ability to list its elements, an operation that succeeds with
high probability for sufficiently large table. However, listing can fail even
for relatively small sets. This paper extends recent work on the worst-case
analysis of IBLT, which guarantees successful listing for all sets of a certain
size, by introducing more general IBLT schemes. These schemes allow for greater
freedom in the implementation of the insert, delete, and listing operations and
demonstrate that the IBLT memory can be reduced while still maintaining
successful listing guarantees. The paper also explores the time-memory
trade-off of these schemes, some of which are based on linear codes and
\(B_h\)-sequences over finite fields.
