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A t-spread in PG(n,q) is a set of distinct t-dimensional subspaces which partition the point set.
A t-parallelism is a partition of the set of t-dimensional subspaces by t-spreads.
Here are the results obtained by Svetlana Topalova and Stela Zhelezova in their investigations on t-spreads and t-parallelisms.
Aut(P) is the full group of automorphisms of the parallelisms.
| Aut(P) | 2 | 3 | 5 | 6 | 7 | 10 | 12 | 13 | 15 | 20 | 24 | 30 | 31 | 48 | 60 | 93 | 96 | 155 | 960 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| PG(3,4) | 8 115 559 ⇓ | 31 830 | 4 488 | 482 | 76 | 52 | - | 40 | 52 | 14 | 38 | - | 12 | 8 | - | 2 | - | 4 | |
| PG(3,5) | 6R | - | 321 duality | 43 | 2R | ||||||||||||||
| PG(5,2) | 1 090 208 | 286 |
| Aut(P) | 2 | 3 | 5 | 7 | 31 | 63 | 155 |
|---|---|---|---|---|---|---|---|
| PG(5,2) | - | 12 220 | 92 |