From planar nearrings to generating blocks (Q543020)

Finite planar nearrings have strong connection with balanced incomplete block designs (BIBDs for short). Several ways of obtaining BIBDs from given finite planar nearrings has been developed [cf. \textit{J. R. Clay}, Nearrings: geneses and applications. Oxford Science Publications. Oxford: Oxford University Press (1992; Zbl 0790.16034)]. In this article, further construction methods are presented. The BIBDs constructed here are the developments of certain subsets of finite fields, referred to as ``zero sum generating blocks.'' These generating blocks are further classified to be of first type and of second type. Then the possible parameters of such BIBDs are discussed thoroughly in two sections.