Minimal Defining Sets of the 3-(12,6,2) Designs – D1

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Design parameters are 3-(12,6,2), b=22

Blocks of the design are:
012348 012567 01369a 01479b 0158ab 02359b 0246ab 02789a 03457a 03678b 045689 1237ab 12459a 12689b 13456b 135789 14678a 234679 23568a 24578b 3489ab 5679ab
The design is simple

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Auto’m group order is 7920

All non-isomorphic minimal defining sets are:

012348 012567 01369a 01479b 02359b
Size=5 |Aut|=2
012567 01369a 01479b 02359b 0246ab
Size=5 |Aut|=10
012348 012567 01479b 02359b 1237ab
Size=5 |Aut|=2
012567 01369a 01479b 02359b 1237ab
Size=5 |Aut|=2

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Size Count
—- —–
5 4

Only 4 (non-isomorphic) minimal defining sets
Totally 12672 (inequivalent) minimal defining sets

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