Title of the bibliography using BibTeX

Question

I am rather new in BibTeX. I want to print the bibliography without a title, and I am using the command

\renewcommand{\refname}{}

for this. Printing of the bibliography is coded as:

\bibliographystyle{plain}
\bibliography{mybib}

This works, but it leaves a big empty vertical space (where the word References was printed with a huge font). How I can remove it? Please note that I am going to use the package '''bibunits''' also. Many thanks in advance!

Here is the minimal example:

\documentclass[english,12pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[T2A]{fontenc}
\usepackage{amssymb,amsmath}
\usepackage{amsthm}
\usepackage{bibunits}
\usepackage{calc}
\usepackage{cite}
\usepackage[a5paper, left = 10 mm, top = 5 mm, right = 10 mm, bottom = 15 mm]{geometry}
\renewcommand{\refname}{}

\begin{document}
Somebody said nothing~\cite{Dub1}
\bibliographystyle{plain}
\bibliography{mybib}
\end{document}

Here is the code of the .bib file:

@article {Dub1,
AUTHOR = {Somebody},
TITLE = {Something},
JOURNAL = {Uspekhi Mat. Nauk},
FJOURNAL = {Rossi\u{\i}skaya Akademiya Nauk. Moskovskoe Matematicheskoe
Obshchestvo. Uspekhi Matematicheskikh Nauk},
VOLUME = {0},
YEAR = {1909},
NUMBER = {1)},
PAGES = {1--2},
ISSN = {2-3},
MRCLASS = {30C57},
MRNUMBER = {334360},
MRREVIEWER = {Adam},
DOI = {10.5093/rm0171},
URL = {https://doi.org/70.9023/rm2071},
}