No candidates have yet reached the quota following the third count for the five Seanad seats from the Cultural and Educational Panel at Dublin Castle.
The count is being live streamed on the Oireachtas social media accounts.
The Returning officer Martin Groves announced the quota was 188,834.
Jack Mulcahy was excluded in the first, Eamonn Walsh was excluded on the second count and Angela Flynn on the third.
Currently, Sinn Féin's Fintan Warfield is top with 151,000 votes, with the Green party's Saoirse McHugh next on 115,00 then Fine Gael Councillor John McGahon with 102,000. In fourth place at this stage Lisa Chambers, former Fianna Fáil TD with 101,000 votes and Sean Kyne, former Fine Gael TD on 82,000 votes.
The boxes were opened at Dublin Castle where strict protocols are in place to prevent the spread of Covid-19.
No media is allowed in and candidates have been asked to stay away.
The Oireachtas Broadcasting service will be providing media outlets with pictures, and news of the results will be available on the Oireachtas social media platforms.
Staff started by dividing out the ballot papers into the five different vocational panels, from which a number of Senators will be elected.
The Cultural and Educational panel from which five Senators will be elected;
Eleven from the Agricultural panel;
The Labour panel will have another 11 Senators elected;
There will be nine seats from the Industrial and Commercial panel;
And finally, seven Senators will be elected from the Administrative panel.
Counting of the ballots for the first panel began this afternoon with the first result expected later tonight.
Oireachtas staff hope to finish each panel by midnight but if not, the count will carry on the following morning.
Tomorrow, the two University panels will begin their count - Trinity is being held in the Dargan lecture theatre, the university's largest room to accommodate social distancing practices.
The National University of Ireland’s count will be held in Shelbourne Hall in the RDS.
Both counts will be streamed online from the universities' websites and there will be six Senators elected, three from each panel.
Those counts are expected to go on for two or three days.
By Friday we will know who 49 of the 60 new Senators are. The next 11 will be nominated by the Taoiseach of the new Dáil, when that is formed.
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Running for a seat in the Seanad on the Cultural and Educational panel are familiar faces from the last Dáil.
Fianna Fáil's Lisa Chambers, who was a surprise loser in the General Election, is running along with party colleagues Margaret Murphy O'Connor, Declan Breathnach and Malcolm Byrne.
Mr Byrne's name is on a fifth ballot paper in less than a year - he fought the European and Local Elections last year, won a seat in the by-election in November only to lose it in the General Election just gone.
The outgoing government chief whip, Sean Kyne, lost his seat and will be hoping to make it back to the Oireachtas with a Seanad seat along with party colleague Tom Neville.
The Green Party's Saoirse McHugh will be hoping for success having failed both the European and General Elections.