This paper presents a digital over-the-air (OTA) computation architecture that reliably aggregates nomographic functions, e.g., sum, product, maximum, and sum-of-squares—over a fading multiple-access channel. Every sensor quantises its reading through a multiple-level amplitude-shift modulation (ASM) hierarchy whose rectangular QAM grids are jointly optimised by a level-wise, maximum-a-posteriori (MAP) search. The optimisation weighs quantization distortion against MAP–detection error, producing the closed-form expression that accommodates both symmetric and asymmetric (weighted) sum. Asymmetric sum is achieved by means of a greatest-common-divisor lattice alignment. In addition, an equal-split quantization is derived for noise-dominated regimes. Numerical results show that: the proposed digital–OTA design surpasses the analog–OTA baseline on three of the four nomographic tasks by up to 20 dB; under heterogeneous node weights the scheme maintains normalised mean square error (NMSE) throughout, whereas analog OTA degrades sharply. These results confirm that ASM-based hierarchical quantization, combined with MAP-optimal grid selection, provides a versatile and spectrally efficient foundation for next-generation edge learning and federated analytics.