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Exponentation-like program on a long tape

I found the following program:

+>+>...+>+> ++...++ [-<[++...++<]>>>[>]<]. (n*"+>", m*"+", l*"+")

This has an output of \((l+1)^{n-1}(lm+1)\) for \(n\geq1\).

This gives, in general \(\mathbf{BF}(2n+m+l+15) \geq (l+1)^{n-1} \cdot (lm+1)\).


n

Lower bound BF(n)

\((l,m,n)\) Program
27 256 \((3,1,4)\)
+>+>+>+>+[-<[+++<]>>>[>]<].
28 625 \((4,1,4)\)
+>+>+>+>+[-<[++++<]>>>[>]<].
29 1024 \((5,1,4)\)
+>+>+>+>+[-<[+++++<]>>>[>]<].
30 3125 \((4,1,5)\)
+>+>+>+>+>+[-<[++++<]>>>[>]<].
31 7776 \((5,1,5)\)
+>+>+>+>+>+[-<[+++++<]>>>[>]<].
32 15625 \((4,1,6)\)
+>+>+>+>+>+>+[-<[++++<]>>>[>]<].
33 46656 \((5,1,6)\)
+>+>+>+>+>+>+[-<[+++++<]>>>[>]<].

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