We announce the discovery of a low-mass planet orbiting the super metal-rich K0V star HD77338 as part of our on-going Calan-Hertfordshire Extrasolar Planet Search . The best fit planet solution has an orbital period of 5.7361 \pm 0.0015 days and with a radial velocity semi-amplitude of only 5.96 \pm 1.74 ms ^ { -1 } , we find a minimum mass of 15.9 ^ { +4.7 } _ { -5.3 } M _ { \oplus } . The best fit eccentricity from this solution is 0.09 ^ { +0.25 } _ { -0.09 } , and we find agreement for this data set using a Bayesian analysis and a periodogram analysis . We measure a metallicity for the star of +0.35 \pm 0.06 dex , whereas another recent work ( ) finds +0.47 \pm 0.05 dex . Thus HD77338 b is one of the most metal-rich planet host stars known and the most metal-rich star hosting a sub-Neptune mass planet . We searched for a transit signature of HD77338 b but none was detected . We also highlight an emerging trend where metallicity and mass seem to correlate at very low masses , a discovery that would be in agreement with the core accretion model of planet formation . The trend appears to show that for Neptune-mass planets and below , higher masses are preferred when the host star is more metal-rich . Also a lower boundary is apparent in the super metal-rich regime where there are no very low-mass planets yet discovered in comparison to the sub-solar metallicity regime . A Monte Carlo analysis shows that this low-mass planet desert is statistically significant with the current sample of 36 planets at \sim 4.5 \sigma level . In addition , results from Kepler strengthen the claim for this paucity of the lowest-mass planets in super metal-rich systems . Finally , this discovery adds to the growing population of low-mass planets around low-mass and metal-rich stars and shows that very low-mass planets can now be discovered with a relatively small number of data points using stable instrumentation .