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This paper reports a blind search for magnetospheric emissions from planets around nearby stars. Young stars are likely to have much stronger stellar winds than the Sun, and because planetary magnetospheric emissions are powered by stellar winds, stronger stellar winds may enhance the radio luminosity of any orbiting planets. Using various stellar catalogs, we selected nearby stars (<~ 30 pc) with relatively young age estimates (< 3 Gyr). We constructed different samples from the stellar catalogs, finding between 100 and several hundred stars. We stacked images from the 74-MHz (4-m wavelength) VLA Low-frequency Sky Survey (VLSS), obtaining 3\sigma limits on planetary emission in the stacked images of between 10 and 33 mJy. These flux density limits correspond to average planetary luminosities less than 5--10 x 10^{23} erg/s. Using recent models for the scaling of stellar wind velocity, density, and magnetic field with stellar age, we estimate scaling factors for the strength of stellar winds, relative to the Sun, in our samples. The typical kinetic energy carried by the stellar winds in our samples is 15--50 times larger than that of the Sun, and the typical magnetic energy is 5--10 times larger. If we assume that every star is orbited by a Jupiter-like planet with a luminosity larger than that of the Jovian decametric radiation by the above factors, our limits on planetary luminosities from the stacking analysis are likely to be a factor of 10--100 above what would be required to detect the planets in a statistical sense. Similar statistical analyses with observations by future instruments, such as the Low Frequency Array (LOFAR) and the Long Wavelength Array (LWA), offer the promise of improvements by factors of 10--100., Comment: 11 pages; AASTeX; accepted for publication in AJ