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|Title:||A nonexistence result on difference sets, partial difference sets and divisible difference sets|
Partial difference sets
|Citation:||Arasu, K.T., Ma, S.L. (2001-05-01). A nonexistence result on difference sets, partial difference sets and divisible difference sets. Journal of Statistical Planning and Inference 95 (1-2) : 67-73. ScholarBank@NUS Repository. https://doi.org/10.1016/S0378-3758(00)00278-0|
|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 Z9×Z27 and (351, 126, 45) difference sets in Z351, thereby filling two missing entries in a recent table of Vera Lopez and Sanchez (1997) both with answer 'no'. © 2001 Elsevier Science B.V.|
|Source Title:||Journal of Statistical Planning and Inference|
|Appears in Collections:||Staff Publications|
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