Efficient survey design for finding high-redshift galaxies with JWST

Several large JWST blank field observing programs have not yet discovered the first galaxies expected to form at $15 \leq z \leq 20$. This has motivated the search for more effective survey strategies that will be able to effectively probe this redshift range. Here, we explore the use of gravitationally lensed cluster fields, that have historically been the most effective discovery tool with HST. In this paper, we analyze the effectiveness of the most massive galaxy clusters that provide the highest median magnification factor within a single JWST NIRCam module in uncovering this population. The results of exploiting these lensing clusters to break the $z > 15$ barrier are compared against the results from large area, blank field surveys such as JADES and CEERS in order to determine the most effective survey strategy for JWST. We report that the fields containing massive foreground galaxy clusters specifically chosen to occupy the largest fraction of a single NIRCam module with high magnification factors in the source plane, whilst containing all multiple images in the image plane within a single module provide the highest probability of both probing the $15 \leq z \leq 20$ regime, as well as discovering the highest redshift galaxy possible with JWST. We also find that using multiple massive clusters in exchange for shallower survey depths is a more time efficient method of probing the $z > 15$ regime.