What database product would support 8000 columns, unlimited row size and no character limit on text fields?

Imagine a spreadsheet that's as wide in column count as it is long in row count - say 10,000 rows x 10,000 columns. That's what I'm trying to find an equivalent DB product to achieve. The column headings also stretch out to about 500 characters but the corresponding cell values on all but 2 of the columns (the first two) are either 1 or 0 (translating a binary data file). So, column 1 and 2 in the structure have conventional string and floating point values and short column names. And then everything else is a 1 or a 0 with the bloated column heading text values taking up more space than the corresponding row values. I have tried SQLite, Postgres, MariaDB and MySQL but I keep running into limits either on the number of columns, on the row size or on the column width (mainly because of the headings). Is there any database product flexible enough to support a single table with all of these features?