Shortest game controlling a single square 16 times?

Question

Does someone know the shortest orthodox chess game such that a single square is directly controlled 16 times? After 1. Nf3 for instance, the square d2 is controlled 5 times. And 2. ... Qa5 pushes the counter to 6. I guess this game (White and Black collaborating) would be around 23-26 moves long?

Answer 1

Addendum #2: It turns out that a move can actually be saved further still! Michel Caillaud wrote on the Retro Mailing List that 19.5 moves is possible!

[Title "Michel Caillaud, Retro Mailing List 9/18/2020, Non-unique Proof Game in 19.5 moves"]
[FEN ""]
[startply "39"]

1. f4 h5 2. f5 h4 3. f6 h3 4. fxe7 hxg2 5. exf8=N Rh6 6. Nh7 a5 7. Nc3 a4 8. e4 a3 9. e5 axb2 10. e6 b1=N 11. e7 Nxd2 12. Nh3 Ne4 13. Nf2 f6 14. Ng4 Kf7 15. Qxd7 Ra6 16. Qd4 Nd7 17. e8=N gxf1=N 18. Nd5 Nfg3 19. Bg5 Nh5 20. Rf1

---

Addendum #1 After some back and forth emailing on The Retro Mailing List last night, Eric Angelini has devised a much shorter game than mine in 20.5 moves! This is surely optimal. Good job Eric!

[Title "Eric Angelini, Retro Mailing List 9/18/2020, Non-unique Proof Game in 20.5 moves"]
[FEN ""]
[startply "41"]

1. a4 d5 2. a5 d4 3. a6 d3 4. axb7 dxc2 5. bxc8=N cxd1=N 6. Nb6 Nf6 7. Na4 Ne4 8. h4 f5 9. h5 f4 10. h6 f3 11. hxg7 fxg2 12. Nf3 g1=N 13. g8=N Nxe2 14. Nxe7 Na6 15. Nd5 Nb4 16. Ra3 Na2 17. Rxh7 Qf6 18. Rxc7 Rh3 19. Rc2 Bb4 20. Nd4 Rc8 21. Nb5

---

For starters, there are a limited number of squares that can be attacked 16 times. A square can only be attacked eight times horizontally and vertically, or four times from each direction. The other eight attacks are from one knight each. A knight can only have its full reach on the central sixteen squares. Therefore, we are restricted to those squares only.

Furthermore, while we have plenty of horizontal and vertical moving pieces in the initial game array, only four knights are present. This means that four more knights must be promoted. The shortest way to do this, theoretically, is to promote 2 knights for both White and Black to split the workload. Promoting four knights already puts us at least 10+ moves in total in addition to the knights' moves to their attacking squares.

Here is my beginning bid of 25.5 moves with the target square of d6.

[FEN ""]
[startply "51"]

1. d4 e5 2. dxe5 d6 3. a4 b5 4. b4 a5 5. axb5 c5 6. Na3 c4 7. Nxc4 Ra6 8. bxa5 Rc6 9. b6 Nd7 10. b7 Nc5 11. a6 h5 12. a7 h4 13. a8=N h3 14. bxc8=N Nb7 15. Nc7+ Kd7 16. Nb5 Qc7 17. Ba3 hxg2 18. h4 Rh6 19. h5 Re6 20. h6 Nf6 21. h7 Ne8 22. h8=N gxf1=N 23. Nxf7 Nd2 24. Nf3 Ne4 25. Nh4 Be7 26. Nf5