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In a previous paper the author found some minimal 1-(v,3) designs with large b, by exhaustive search. Here some further such are found, by more ad-hoc methods. A construction is given for v = 3t+1 for t ≥ 2, where b grows quadratically with v. AMS Subject Classification: 05B05

A LOWER BOUND ON THE LENGTH OF BASIC MINIMAL 1-(3t+1,3) DESIGNS