Geodesic
A study of $k$-arcs in Hughes plane of order 9 by means of computer
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 28-38 
V. I. Vasil'kov; G. V. Maslennikov. A study of $k$-arcs in Hughes plane of order 9 by means of computer. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 5 (1998), pp. 28-38. http://geodesic.mathdoc.fr/item/TIMM_1998_5_a1/
@article{TIMM_1998_5_a1,
     author = {V. I. Vasil'kov and G. V. Maslennikov},
     title = {A study of $k$-arcs in {Hughes} plane of order~9 by means of computer},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {28--38},
     year = {1998},
     volume = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_1998_5_a1/}
}
TY  - JOUR
AU  - V. I. Vasil'kov
AU  - G. V. Maslennikov
TI  - A study of $k$-arcs in Hughes plane of order 9 by means of computer
JO  - Trudy Instituta matematiki i mehaniki
PY  - 1998
SP  - 28
EP  - 38
VL  - 5
UR  - http://geodesic.mathdoc.fr/item/TIMM_1998_5_a1/
LA  - ru
ID  - TIMM_1998_5_a1
ER  - 
%0 Journal Article
%A V. I. Vasil'kov
%A G. V. Maslennikov
%T A study of $k$-arcs in Hughes plane of order 9 by means of computer
%J Trudy Instituta matematiki i mehaniki
%D 1998
%P 28-38
%V 5
%U http://geodesic.mathdoc.fr/item/TIMM_1998_5_a1/
%G ru
%F TIMM_1998_5_a1

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Using the method of step-by-step identifications, as well as a computer, authors study $k$-arcs of Hughes plane of order 9 for $k=3, 4,\dots, 10$. The following results are obtained. For $k=6,7,8$, and 9 there are 1720, 1427, 24, and 4 types of incomplete $k$-arcs, respectively. There are 198 types of complete 7-arcs and 316 types of complete 8-arcs. For $k=3,4,5$ and for some types of 6-arcs, our results repeat the earlier ones of V. I. Vasil'kov. The results concerning complete $k$-arcs for $k=6,9,10$ coincide with those of Denniston (1971). For $k$-arcs of each type, the group of automorphisms is described and the total number of aires is found which are isomorphic to a given arc with respect to the group of all collineations in Hughes plane of order 9.