Orthogonal frequency division multiplexing with subcarrier number modulation (OFDM-SNM) has been recently proposed to improve the spectral efficiency (SE) of the traditional OFDM system. In this paper, we propose a joint-mapping OFDM-SNM (JM-OFDM-SNM) scheme to transmit the signal vector with a constant length of information bits by jointly considering the subcarrier activation patterns and constellation symbols. A low-complexity detection scheme based on log-likelihood ratio criterion is proposed to relieve the high computational complexity of the maximum-likelihood detection at the cost of a negligible performance loss. Upper-bounded bit error rate (BER) and lower-bounded achievable rate are both derived in closed-form to evaluate the performance of JM-OFDM-SNM. To suit different application scenarios, we further propose two enhanced schemes, named adaptive JM-OFDM-SNM (AJM-OFDM-SNM) and JM-OFDM with in-phase/quadrature SNM (JM-OFDM-IQ-SNM), where the former adjusts the constellation orders for different numbers of active subcarriers, and the latter extends the indexing to in-phase and quadrature domains. Simulation results corroborate the tightness of the derived BER expression in the high signal-to-noise ratio region and show that (A)JM-OFDM-SNM improves the performance of OFDM-SNM, while both AJM-OFDM-SNM and JM-OFDM-IQ-SNM schemes perform better than JM-OFDM-SNM at the same SE.