The following are the initial blocks for a nested design in which the main blocks comprise a 3-design(12,165,110,8,42) and the sub-blocks comprise a 3-design(12,330,110,4,6). This was obtained by trial-and-error from a Mathieu design. ∞ denotes an invariant treatment.

(2 3 6 8 | 9 7 5 4) (8 1 2 10 | 3 6 9 5)

(10 4 8 7 | 1 2 3 9) (7 5 10 6 | 4 8 1 3)

(6 9 7 2 | 5 10 4 1) (5 8 2 ∞ | 10 3 9 7)

(9 10 8 ∞ | 7 1 3 6) (3 7 10 ∞ | 6 4 1 2)

(1 6 7 ∞ | 2 5 4 8) (4 2 6 ∞ | 8 9 5 10)

(∞ 6 5 0 | 8 2 10 9) (∞ 2 9 0 | 10 8 7 3)

(∞ 8 3 0 | 7 10 6 1) (∞ 10 1 0 | 6 7 2 4)

(∞ 7 4 0 | 2 6 8 5)

developed mod 11