A note on balanced (q, {3, 4}, λ)-DFs with q a prime power
نویسندگان
چکیده
In this note, it is proved that the necessary and sufficient conditions for the existence of a balanced (q, {3, 4}, λ)-DF over GF (q) are q ≥ 4 and q ≡ 1 (mod 18 gcd(18,λ) ).
منابع مشابه
A note on the existence of balanced (q, {3, 4}, 1) difference families
A (v,K, λ) difference family ((v,K, λ)-DF in short) can be used to construct a (v,K, λ)-PBD. A lot of work has been done on the existence of (v, k, 1) difference families ((v, k, 1)-DF in short) when K = {k} is a singleton. For K = {3, 4}, partial results have been obtained by Buratti. In this paper, it is proved that there exists a balanced (q, {3, 4}, 1)-DF for each prime power q ≡ 1 (mod 18).
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 50 شماره
صفحات -
تاریخ انتشار 2011