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We construct many new cyclic (v;r,s;lambda) difference families with v lessthan or equal 50. In particular we construct the difference families withparameters (45;18,10;9), (45;22,22;21), (47;21,12;12), (47;19,15;12),(47;22,14;14), (48;20,10;10), (48;24,4;12), (50;25,20;20) for which theexistence question was an open problem. The (45;22,22;21) difference familygives a BIBD with parameters v=45, b=90, r=44, k=22 and lambda=21, and the onewith parameters (50;25,20;20) gives a pair of binary sequences of length 50with zero periodic autocorrelation function (the periodic analog of a Golaypair). We also construct nine new D-optimal designs. A normal form for cyclicdifference families is proposed and used effectively in compiling the list ofknown and new difference families.

Cyclic (v;r,s;lambda) difference families with two base blocks and v <= 50