Minimal Defining Sets of the 2-(16,6,2) Designs – D3

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

Blocks of the design are:
0127bf 0136ae 02569d 034cdf 0489be 0578ac 123458 1479ad 15bcde 1689cf 2379ce 246abc 28adef 359abf 3678bd 4567ef
The design is simple

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Auto’m group order is 384

All non-isomorphic minimal defining sets are:

0127bf 0136ae 02569d 034cdf 0489be 123458 2379ce
Size=7 |Aut|=1
0127bf 0136ae 02569d 0489be 0578ac 123458 2379ce
Size=7 |Aut|=1
0127bf 02569d 034cdf 0489be 0578ac 123458 2379ce
Size=7 |Aut|=1
0127bf 0136ae 02569d 034cdf 123458 1479ad 2379ce
Size=7 |Aut|=1
0127bf 0136ae 02569d 0489be 123458 1479ad 2379ce
Size=7 |Aut|=1
0127bf 02569d 034cdf 0578ac 123458 1479ad 2379ce
Size=7 |Aut|=1
0136ae 02569d 034cdf 0578ac 123458 1479ad 2379ce
Size=7 |Aut|=1
0127bf 034cdf 0489be 0578ac 123458 1479ad 2379ce
Size=7 |Aut|=1
0127bf 02569d 034cdf 123458 1479ad 15bcde 2379ce
Size=7 |Aut|=1
0127bf 0136ae 0489be 0578ac 123458 2379ce 246abc
Size=7 |Aut|=3

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Size Count
—- —–
7 10

Only 10 (non-isomorphic) minimal defining sets
Totally 3584 (inequivalent) minimal defining sets

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