5-Designs with three intersection numbers

It is well known that the Witt 5-(24, 8, 1) design and its complement have exactly three block intersection numbers. This paper is concerned with the converse question: Is the Witt 5-(24,8, 1) design the unique 5-(ν, k, λ) design (up to complements) with exactly three intersection numbers? Using the annihilator polynomial of such a design, we prove that the answer is affirmative if k − 1 is a prime or λ ≤ 4 or at least two intersection numbers are less than 5. Numerical evidence using MAPLE seems to support that the answer is always yes.