Strong radar reflections have been previously mapped at the base of the Martian South Polar Layered Deposits (SPLD). Here, we analyze laboratory measurements of dry and briny samples to determine the cause of this radar return. We find that liquid vein networks consisting of brines at the grain boundaries of ice crystals can greatly enhance the electrical conductivity, thereby causing strong radar reflection. A liquid brine concentration of 2.7–6.0 vol% in ice is sufficient to match the electrical properties of the basal reflection as observed by MARSIS. When brine is mixed with sediments, we find that the brine-ice mixture in the pores must be 2–5 times more concentrated in salt, increasing the brine concentration to 6.3–29 vol%. Thus, our best fit of the median observed MARSIS value suggests a salt-bulk sample concentration of ~6 wt%, which is ~8 larger than that of the Phoenix landing site. To form brine, the basal reflector must reach a temperature greater than the eutectic temperature of calcium perchlorate of 197.3±0.2 K. Colder metastable brines are possible, but it is unclear if brines can remain metastable for millions of years. Additionally, grey hematite with a concentration of 33.2-59.0 vol% possess electrical properties that could cause the observed radar returns. However, such concentrations are 2-3 times larger than anywhere currently mapped on Mars. We also demonstrate that brines mixed with high-surface-area sediments, or dry red hematite, jarosite, and ilmenite cannot create the observed radar returns at low temperatures.