No.

Known Symmetric BIBDs

Number of Disjoint BIBDs

1

$v=7,b=7,r=3,k=3,\lambda =1$

2

2

$v=13,b=13,r=4,k=4,\lambda =1$

3

3

$v=21,b=21,r=5,k=5,\lambda =1$

4

4

$v=31,b=31,r=6,k=6,\lambda =1$

5

4

$v=57,b=57,r=8,k=8,\lambda =1$

7

5

$v=73,b=73,r=9,k=9,\lambda =1$

8

6

$v=7,b=7,r=4,k=4,\lambda =2$

2

7

$v=11,b=11,r=5,k=5,\lambda =2$

3

8

$v=16,b=16,r=6,k=6,\lambda =2$

4

9

$v=15,b=15,r=7,k=7,\lambda =3$

4

10

$v=19,b=19,r=9,k=9,\lambda =4$

5