Most methods for sound field reconstruction and spherical beamforming with spherical microphone arrays are mathematically based on the spherical harmonics expansion. In many cases, this expansion is truncated at a certain order as in higher order ambisonics (HOA). This truncation leads to performance that is independent of the incident direction of the sound waves. On the other hand, mixed-order ambisonic (MOA) schemes that select an appropriate subset of spherical harmonics can improve the performance for horizontal directions at the expense of other directions. This paper proposes an MOA scheme called Periphony-Lattice to improve sound field reconstruction performance for horizontally incident sound waves. The proposed scheme is compared with the previously introduced MOA and HOA schemes in terms of theoretical truncation error and performance in sound field reconstruction and spherical beamforming. Computer simulations and measurements are conducted with a spherical array of 52 microphones with a nonuniform layout. The results show that the proposed MOA scheme has better performance in sound field reconstruction and spherical beamforming for horizontal sound waves than the other schemes for a given number of microphones. This scheme can be applied to other spherical array layouts if the number of microphones is greater than that of the required spherical harmonics coefficients, and may improve the horizontal performance.