There is no way to improve your brain activity directly. But some behaviors are expected to maintain your mind healthy and energetic: high-qualified sleep, balanced meal, and physical exercise.
Then, what kind of exercise is the best for your brain? I have no idea. To begin with, evaluating the influence of exercise on your health itself is not an easy task. Comparing the effect of each exercise is almost impossible.
It is certain that aerobic exercises seem superior to non-aerobic ones for reducing your body weight. But each kind of activity has perhaps their own benefits. For example, the writer of this article above recommends you to take martial arts.
The Conversation: Five brain-boosting reasons to take up martial arts – at any age
Indeed, several studies have been conducted suggesting the benefits of martial arts. I admire the efforts of the researchers to evaluate the precise effect of playing martial arts. However, it does not suggest martial arts is the best exercise, but martial arts are widespread in the US, one of the nations many qualified studies are made. In China, Tai-kyoku-ken (Chinese shadow boxing) is commonly used for elder people to maintain their health. Some Japanese researchers might believe Judo Karate makes your body and mind fresh and enhanced.
As well, the effect on your body and mind of exercise depends on the quality level of each activity. Many people play basketball. But the amount of consumed energy for one game differ by three times between amateur and semi-professional player, I have heard from a researcher of industrial health.
After all, you may choose some exercise you would like to do. Continuous activity is essential for the health benefit regardless of the kind of practice.