Introduction: Color transformations are widely used in television systems. One of the most popular and demanded ways to implement color transformations are three-dimensional lookup tables. At the same time, the existing methods of creating lookup tables are characterized with a number of drawbacks. Purpose: To develop an analytical method for constructing optimized three-dimensional lookup tables with specified properties (providing smoothness of transformation, possibility of construction at incomplete coverage of mapped spaces by initial data, etc.) and taking into account the existing drawbacks in regularization approaches. Results: We propose a new analytical method for constructing optimized lookup tables for color transformations. The method provides obtaining optimized tables, which by their characteristics correspond or surpass the non-optimized tables with the size corresponding to the next step n (N = 2n + 1) and at the same time provide better smoothness of transformation. Compared to state-of-the-art counterparts used in television systems for color transformations, the method exhibits 1.5 to 2 times lower mean error and 1.5 to 4 times lower 95% error percentile. The method provides high accuracy of color transformations and has good manufacturability due to obtaining an analytical solution. Providing better accuracy compared to similar methods of optimized table construction, the proposed method keeps the table lattice in the prototype regular and uniform, which makes the construction process faster, and the table itself is significantly more efficient and easier to use when implemented in real devices. Practical relevance: The method can be applied in the development of television systems where high color reproduction accuracy is required.