Minimal Defining Sets of the 2-(16,6,2) Designs – D1

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Design parameters are 2-(16,6,2), b=16

Blocks of the design are:
0127bf 0136ae 02359d 048def 049abc 05678c 12348c 14679d 158abd 159cef 2457ae 2689be 26acdf 3456bf 3789af 37bcde
The design is simple

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Auto’m group order is 11520

All non-isomorphic minimal defining sets are:

0127bf 0136ae 02359d 048def 049abc 14679d 158abd 2457ae 2689be
Size=9 |Aut|=8
0136ae 02359d 049abc 05678c 12348c 14679d 158abd 2457ae 2689be
Size=9 |Aut|=72
0127bf 0136ae 02359d 048def 049abc 12348c 14679d 159cef 2457ae 2689be
Size=10 |Aut|=60

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Size Count
—- —–
9 2
10 1

Only 3 (non-isomorphic) minimal defining sets
Totally 1792 (inequivalent) minimal defining sets

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