On inequivalent balanced incomplete block designs, II

Abstract

The existence of at least two inequivalent designs has been established for balanced incomplete block designs with parameters

$$\text{m}{}^{\mathrm{q}}\text{,}\text{m}{}^{\mathrm{q-1}}\text{(m}{}^{\mathrm{q}}\text{−1)}\text{m−1}\text{,}\text{m}{}^{\mathrm{q}}\text{−1}\text{m−1}\text{,m,1}\text{,q⩽4,m⩽4}\text{and}$$

q = 3, m ⩾ 6, where m is a prime power. It is also proved that the number of inequivalent configurations with these parameters tends to infinity along with q.