Abstract
Cameron-Liebler line classes are sets of lines in PGð3; qÞ that contain a fixed number x of lines of every spread. Cameron and Liebler classified them for x A f0; 1; 2; q 2 � 1; q 2 ; q 2 þ 1g and conjectured that no others exist. This conjecture was disproven by Drudge and his counterexample was generalised to a counterexample for any odd q by Bruen and Drudge. Nonexistence of Cameron-Liebler line classes was proven for dierent values of x by Penttila, Bruen and Drudge, Drudge, and Govaerts. In this paper, a new lower bound on x for existence of Cameron-Liebler line classes is obtained, and in the specific cases where q is a square or a cube, this new bound is improved upon.
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