  In CI-Liaison, significant effort has been made to study ideals that are in
the linkage class of a complete intersection, which are called licci ideals. In
a polynomial ring, recently E. Chong defined a "sequentially bounded" condition
on the degrees of the forms generating the regular sequences, and used this
condition to find a large class of licci ideals satisfying the
Eisenbud-Green-Harris Conjecture (among them, grade $3$ homogeneous Gorenstein
ideals). He raised the question of whether all homogeneous licci ideals are
sequentially bounded licci. In this paper we construct a class of examples that
are homogeneously licci, but not sequentially bounded licci, thus answering his
question in the negative. The structure of certain Betti tables plays a central
role in our proof.
