On resolvability of Steiner systems S ( v = 2 m , 4, 3) of rank r ≤ v − m + 1 over <img src="/fulltext-image.asp?format=htmlnonpaginated&src=C711667638135KQR_html\11122_2007_Article_1005_TeX2GIFIE1.gif" border="0" alt=" $$\mathbb{F}_2 $$ " />

Abstract&#160;&#160;Two new constructions of Steiner quadruple systems S(v, 4, 3) are given. Both preserve resolvability of the original Steiner system and make it possible to control the rank of the resulting system. It is proved that any Steiner system S(v = 2 m , 4, 3) of rank r ≤ v − m + 1 over F2 is resolvable and that all systems of this rank can be constructed in this way. Thus, we find the number of all different Steiner systems of rank r = v − m + 1. [ABSTRACT FROM AUTHOR]