From the opening position for black (with no white pieces on the board), what is the fewest number of moves in which we can dominate the entire board, that is, reach a position so that each square is either attacked by, or occupied by, a black piece?

This is a question which has arisen from a similar question on Puzzling Stack Exchange.

Over there, we found that it could be achieved in 11 moves and very nearly could be achieved in 10.

For example, in the final position below we see that the only square which is neither attacked nor occupied is e4 which is right in front of a pawn. This is close enough to make me suspect that it might be achievable in 10.

[FEN "rnbqkbnr/pppppppp/8/8/8/8/8/8 w kq - 0 1"]

1. null d5 2. null d4 3. null d3 4. null d2 5. null d1=Q 6. null Q8d2 7. null h5 8. null h4 9. null b5 10. null e5

In this case, we can achieve domination in one extra move by 11. null Nf6

Paul Panzer found some other sequences which come close to achieving domination in 10 moves.

[FEN "rnbqkbnr/pppppppp/8/8/8/8/8/8 w kq - 0 1"]

1. null h5 2. null h4 3. null h3 4. null h2 5. null h1=Q 6. null Rh3 7. null e5 8. null Qg5 9. null Qd2 10. null b5 11. null d5

And another:

[FEN "rnbqkbnr/pppppppp/8/8/8/8/8/8 w kq - 0 1"]

1. null a5 2. null a4 3. null a3 4. null a2 5. null a1=Q 6. null Qb2 7. null Ra1 8. null e5 9. null Qg5 10. null d5 11. null e4

It seems to me that the answer to this question would have been analysed before and the answer may be well know among chess enthusiasts but I have yet to find it.

Can it be achieved in 10 moves?
If so, what is the fewest number of moves required?
If not, is there a proof of this fact?

P.S. I thought it more appropriate to post the question here rather than on Puzzling Stack Exchange because there will be a greater familiarity with the opening position here and a greater pool of suitable knowledge from which to draw (although there is a healthy overlap between the two sites).

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