No.

Known Symmetric BIBDs

Designs that Can Be Constructed through Combination Method

1

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

$v=7,b=14,r=6,k=3,\lambda =2$

2

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

$v=13,b=26,r=8,k=4,\lambda =2$

$v=13,b=39,r=12,k=4,\lambda =3$

3

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

$v=21,b=42,r=10,k=5,\lambda =2$

$v=21,b=63,r=15,k=5,\lambda =3$

$v=21,b=84,r=20,k=5,\lambda =4$

4

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

$v=31,b=62,r=12,k=6,\lambda =2$

$v=31,b=93,r=18,k=6,\lambda =3$

$v=31,b=124,r=24,k=6,\lambda =4$

$v=31,b=155,r=30,k=6,\lambda =5$

5

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

$v=57,b=114,r=16,k=8,\lambda =2$

$v=57,b=171,r=24,k=8,\lambda =3$

$v=57,b=228,r=32,k=8,\lambda =4$

$v=57,b=285,r=40,k=8,\lambda =5$

$v=57,b=342,r=48,k=8,\lambda =6$

$v=57,b=399,r=56,k=8,\lambda =7$