BLT-sets over small fields

A BLT-set is a set X of q+l points of the generalized quadrangle Q(4, q), q odd, such that no point of Q(4, q) is collinear with more than 2 points of X. BLT-sets are closely related to flocks of the quadratic cone, elation generalised quadrangles and certain translation planes. In this paper we report on the results of computer searches for BLT-sets for odd q ::; 25. We complete the classification for q ::; 17 finding one new BLT-set, and provide further examples for q = 19, q = 23 and q = 25 finding 10 new BLT-sets altogether. The relationship between BLT-sets and flocks of the quadratic cone in PG(3, q) means that this work classifies flocks for q ::; 17 and finds new flocks for q = 19, q = 23 and q = 25. In total the 10 new BLT-sets yield 26 new flocks.