Does LTE support 256 QAM?

The required bandwidth is related to bit rate and the modulation order M. It is so that the double sided bandwidth w = symbol rate= bit rate rb/ divided by the number of bit per symbol n . The number of bits per symbol is = log 2M with M is the M is the QAM modulation order.

One of the LTE features introduced in Rel-12 is the support for higher order modulation, that is 256QAM for DL data transmission to enhance the spectral efficiency and the system throughput.

From Rel 12 , 3GPP defines (support) 256 QAM in Downlink.

Just what is QAM-256? It refers to Quadrature Amplitude Modulation , which is the means by which a carrier signal, such as an LTE waveform, transmits data and information. Ideally, a waveform/symbol carries as much data as possible in order to achieve higher data rates and increase spectral efficiency.