Abstract: The design of large scale, high numerical aperture, and broadband achromatic flat lens is a bottleneck of imaging technology and also a big challenge in metalens researches in recent years. The major reason is that there are some internal constraints between these parameters. In this paper, considering both the group dispersion theory and the phase distribution of the flat lens, the semi-quantitative relationship between these parameters was derived. Then, the achromatic flat lenses (including metalenses and multi-level diffractive lenses) with different parameters were designed by using directly binary search and topology optimization. It was found that under the condition of maintaining an efficiency of 80%, when doubling the size of flat lens (i.e., the diameter), the numerical or achromatic bandwidth was cut in half, and the thickness of lens increased linearly with lens scale. The results definitely show that these two types of flat lenses have the same internal constraint relations in parameters, that is, as that the lens size has negative correlation with the numerical aperture and achromatic bandwidth, while positive correlation with the thickness of the lenses. This result is in coincidence with the theoretical prediction.