Minimal Defining Sets of the 2-(8,4,3) Designs – D4

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Design parameters are 2-(8,4,3), b=14

Blocks of the design are:
0123 0145 0167 0246 0257 0347 0356 1247 1256 1346 1357 2345 2367 4567
The design is simple

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Auto’m group order is 1344

All non-isomorphic minimal defining sets are:

0123 0145 0246 0257 0347 1247 1256 1346
Size=8 |Aut|=8
0257 0347 0356 1247 1256 1346
Size=6 |Aut|=48

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Size Count
—- —–
6 1
8 1

Only 2 (non-isomorphic) minimal defining sets
Totally 196 (inequivalent) minimal defining sets

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