Finite Projective Planes and Orthogonal Arrays

我们得到了以下四个结果。（1）这是一个没有预测的订单12个集合组的订单16由展示一些正统数组OA （72，12，6，2）。我们使用了一台计算机进行研究。（2）它被证明只有一个对称性的跨相设计STD_4[12;3]符合异构性。我们还展示了STD_4[12;3]的完整自晶组的顺序是2^5和3^3，而STD_4[12;3]在点设置上有一个常规亚组作为渗透组。我们使用了一台计算机进行研究。（3）We constructed a symmetric transversal sesign STD_7 [21;3] admitting an automorphism group of order 7 which acts semiregularly on the set of the point groups and on the set of block groups。（4）让我们在算术投影平面上做一个阻塞半数的序列，9在8点遇到一些线条。According to Dover in [2]，20 leqvert Svertleq 24。在[7]一位作者展示说，如果Pi是反argesian，那么22个leqvert Svertleq 24。在这篇文章中，所有阻塞的半导体都与此财产在所有非德索经济预测平面的第9号完全被确定。在任何非反西班牙平面上，它都显示了21个字母Svertleq 24和每个硬币{21，22，23，24}在8点内存在着阻塞半尺寸我遇到的几条线。因此，多佛的界限并不清晰。

We got the following four results.(1)It was proved that there is no projective plane of order 12 admitting a collineation group of order 16 by showing the nonexistence of some orthogonal array OA (72,12,6,2). We used a computer for our research.(2)It was proved that there is only one symmetric transversal design STD_4[12;3] up to isomorphism. We also showed that the order of the full automorphism group of STD_4[12;3] is 2^5・3^3 and Aut STD_4[12;3] has a regular subgroup as a permutation group on the point set. We used a computer for our research.(3)We constructed a symmetric transversal sesign STD_7[21;3] admitting an automorphism group of order 7 which acts semiregularly on the set of the point groups and on the set of block groups.(4)Let S be a blocking semioval in arbitrary projective plane Pi of order 9 which meets some line in 8 points. According to Dover in [2], 20leqvert Svertleq 24. In [7] one of the authors showed that if Pi is desarguesian, then 22leqvert Svertleq 24. In this note all blocking semiovals with this property in all non-desarguesian projective plane of order 9 are completely determined. In any non-desarguesian plane Pi it is shown that 21leqvert Svertleq 24 and for each iin{21,22,23,24} there exist blocking semiovals of size I which meet some line in 8 points. Therefore, the Dover's bound is not sharp.