Minimal Defining Sets of the 3-(8,4,2) Designs – D1

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Design parameters are 3-(8,4,2), b=28

Blocks of the design are:
0124 0124 0137 0137 0156 0156 0235 0235 0267 0267 0346 0346 0457 0457 1236 1236 1257 1257 1345 1345 1467 1467 2347 2347 2456
2456 3567 3567
The design is not simple, with support 14

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Auto’m group order is 1344

All non-isomorphic minimal defining sets are:

0124 0124 0137 0137 0235 0235
Size=6 |Aut|=6

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Size Count
—- —–
6 1

Only 1 (non-isomorphic) minimal defining set
Totally 224 (inequivalent) minimal defining sets

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