Binary amplitude modulation promises to allow rapid focusing through strongly scattering media with a large number of segments due to the faster update rates of digital micromirror devices (DMDs) compared to spatial light modulators (SLMs). While binary amplitude modulation has a lower theoretical enhancement than phase modulation, the faster update rate should more than compensate for the difference – a factor of π2 /2. Here we present two new algorithms, a genetic algorithm and a transmission matrix algorithm, for optimizing the focus with binary amplitude modulation that achieve enhancements close to the theoretical maximum. Genetic algorithms have been shown to work well in noisy environments and we show that the genetic algorithm performs better than a stepwise algorithm. Transmission matrix algorithms allow complete characterization and control of the medium but require phase control either at the input or output. Here we introduce a transmission matrix algorithm that works with only binary amplitude control and intensity measurements. We apply these algorithms to binary amplitude modulation using a Texas Instruments Digital Micromirror Device. Here we report an enhancement of 152 with 1536 segments (9.90%×N) using a genetic algorithm with binary amplitude modulation and an enhancement of 136 with 1536 segments (8.9%×N) using an intensity-only transmission matrix algorithm.