Abstract
Abstract A new nonexistence theorem is proved for abelian difference sets. The proof technique generalizes to yield similar theorems for partial and divisible difference sets. As applications, we establish the nonexistence of two previously open difference sets: (243, 121, 60) difference sets in Z 9 × Z 27 and (351, 126, 45) difference sets in Z 351 , thereby filling two missing entries in a recent table of Vera Lopez and Sanchez (1997) both with answer ‘no’.
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