A new technique is developed to globally identify and optimize all useful idealized Earth-Mars cyclers constructed with Earth-Earth free returns patched by gravity-assisted flybys. Previous techniques that use solutions of the multiple-revolution Lambert problem are expanded. Using combinatorics, the entire solution space is investigated for combinations of generic, half-revolution, and full-revolution free-return transfers for cyclers with periods up to three synodic periods. All three types of free returns are generalized to include the possibility for multiple revolutions. Multiple options for the short Earth-Mars and Mars-Earth legs that characterize the cyclers are included. The generalized technique requires the solutions to hundreds of thousands of minimax optimization problems and results in 142 previously undocumented ballistic cyclers. In addition, the global search verifies and encompasses results from several earlier studies that looked at a variety of subsets of the current solution space. The final list is exhaustive for the defined class of cyclers and is an excellent resource for future researchers that seek cyclers in a more realistic solar system.
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