The programmable delay line is one of the key components in automatic test equipment. Recently, implementation of programmable delay lines on FPGAs has drawn growing attention due to the flexibility and reconfiguration capability that FPGAs provide. In this work, we propose the subset sum delay line (SSDL) architecture for FPGA-based delay lines. The SSDL architecture takes advantage of the inevitable FPGA process variations, structure irregularities and routing uncertainties to realize high-quality FPGA-based delay lines. Furthermore, compared to previous FPGA-based delay lines, the SSDL architecture is FPGA independent, this substantially enhances its portability across different FPGA generations and suppliers. An SSDL is realized on Alter a Cyclone II FPGA. Measurement results show that it achieves 76 ps resolution and has a dynamic range of 32 ns.