  The problem of sparse representation has significant applications in signal
processing. The spark of a dictionary plays a crucial role in the study of
sparse representation. Donoho and Elad initially explored the spark, and they
provided a general lower bound. When the dictionary is a union of several
orthonormal bases, Gribonval and Nielsen presented an improved lower bound for
spark. In this paper, we introduce a new construction of dictionary, achieving
the spark bound given by Gribonval and Nielsen. Our result extends Shen et al.'
s findings [IEEE Trans. Inform. Theory, vol. 68, pp. 4230--4243, 2022].
