This paper investigates the implementation of high-radix multiplication based on the electron counting (EC) paradigm in single electron tunneling (SET) technology. First we propose a multiplication scheme which conceptually speaking follows the structure of traditional full-tree multipliers. The high-radix EC multiplication scheme comprises three steps and of each an implementation is presented. Second, an 8-bit radix 4 EC multiplier is designed and verified by means of simulation. The high-radix multiplication scheme is evaluated in terms of area and delay for different operand sizes and compared with corresponding binary multiplication schemes in SET technology. Both type of implementations prove to have similar delay times, but the EC based scheme requires up to five times less area