Minimal Defining Sets of the 2-(10,4,2) Designs – D1

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Design parameters are 2-(10,4,2), b=15

Blocks of the design are:
0123 0147 0258 0369 0456 0789 1269 1358 1489 1567 2347 2468 2579 3459 3678
The design is simple

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Auto’m group order is 720

All non-isomorphic minimal defining sets are:

0123 0147 0258 0369 0456 1269 1489 2468
Size=8 |Aut|=2
0123 0258 0369 0456 1269 1358 1489 2468
Size=8 |Aut|=8
0147 0258 0369 0456 1269 1358 1489 2468
Size=8 |Aut|=2
0147 0258 0369 0789 1269 1358 1567 2468
Size=8 |Aut|=8
0123 0147 0369 0456 0789 1269 1358 1567 2468
Size=9 |Aut|=6

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Size Count
—- —–
8 4
9 1

Only 5 (non-isomorphic) minimal defining sets
Totally 1020 (inequivalent) minimal defining sets

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