Explicit difference families and block lists are given for new point-transitive Steiner systems S(2,6,111), S(2,6,121), S(2,6,126), S(2,7,169), and S(2,7,175), including an exhaustive count of 30 systems on 111 points.
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Point-transitive Steiner systems S(2,6,111/121/126), S(2,7,169/175)
Explicit difference families and block lists are given for new point-transitive Steiner systems S(2,6,111), S(2,6,121), S(2,6,126), S(2,7,169), and S(2,7,175), including an exhaustive count of 30 systems on 111 points.