Hi, here are some of my ideas for your consideration:
#16 and #17 are wordmarks that show a numeral 1 hidden within the text. In #16, it's in the negative space of the U and in the #17 it is the letter i itself. The idea here was to tie the concepts of oneness and singularity as implied by the use of prefix "uni" in the company name.
#18 and #19 are wordmarks that merge the U and N together into a single shape to imply unity.
#20 is an abstract mark made up of the letters U and N connected and repeated in a star-like pattern.
#18 and #19 seem incomplete, perhaps you can expand on it, make it a little fancier. #20 might be better in other colors. F.Y.I: The Uni in Unibase stands for UNIX, so historically the name Unibase Solutions came from UNIX and Database Solutions.