  Antenna arrays have many applications in direction-of-arrival (DOA)
estimation. Sparse arrays such as nested arrays, super nested arrays, and
coprime arrays have large degrees of freedom (DOFs). They can estimate large
number of sources greater than the number of elements. They also have closed
form expressions for antenna locations and the achievable DOFs. The multi-level
prime array (MLPA) uses multiple uniform linear subarrays where the number of
elements in the subarrays are pairwise coprime integers. The array achieves
large DOFs and it has closed form expressions for the antenna locations and the
required aperture size. For a given number of subarrays and total number of
elements, there are different design alternatives. This paper finds the optimum
number of elements within each subarray and the optimized ordered inter-element
spacing. In almost all cases, we have found that a unique configuration jointly
realizes the maximum number of unique lags and the maximum number of
consecutive lags.
