Albert has many cows. He wishes to identify the cows by giving each one an $11$-bead bracelet. Each bracelet will contain one bead marked with a positive integer. However, Albert can only use numbers up to (and including) $100$ or the cows will get confused.
Additionally, Albert is free to choose from $3$ colors for each of the $11$ beads. If Albert wishes to make each bracelet unique, regardless of any rotations or flips that might occur as the cows roam about, what is the maximum number of cows he can tag?