Waterloo Sunrise said:
4 times as many nations took part in sailing as there were total competitors in women's BMX.
In track cycling both the men's and women's omnium and keirin had 18 participants, men's sprint had 17. A few other events also had 17 or 18 participants as well.
Women's BMX had the same number of participants as:
Taekwondo - all 4 mens' and all 4 womens' categories.
Trampoline - both mens' and womens'.
And more participants than:
Boxing - Mens' heavy (15), Womens' fly (12), Womens' light (12), Womens' middle (12).
Weightlifting - Mens' 62kg (15), Mens' 77kg (12), Womens' 48kg (14), Womens' 63kg (10), Womens' 69kg (15), Womens' 75kg (13), Womens' 75kg+ (14).
Throw in some wrestling categories as well, I got bored of counting.
All this to say that BMX isn't the event with the least participants, and the only reason it had only 16 is because the IOC-UCI decided to cut it at that, not because there wasn't enough talent available, unlike in some of the aforementioned medal events.