Validity of Lander’s Conjecture for \(\lambda\) = 3 and \(k \leq 500\)

Lander Conjectured: If \(D\) is a \((\text{v, k}, \lambda)\) difference set in an abelian group G with a cyclic Sylow p-subgroup, then p does not divide \((v, n)\), where \(\text{n} = \text{k} – \lambda \).

In a previous paper, the above conjecture was verified for \(\lambda = 3\) and \(\text{k} \leq 500\), except for \(\text{k} = 228, 282\) and \(444\). These three exceptional values are dealt with in this note, thereby verifying Lander’s conjecture completely for \(\lambda = 3\) and \(\text{k} \leq 500\).