The order was set by lottery Friday. Today the luckiest lottery “winners” will start to pick where they want to live in a moderately priced condominium tower slated to rise later this year in Kakaako.

The Ke Kilohana tower at Ward Village will have 375 units reserved for residents with incomes not too far above the median in Honolulu, and it attracted 956 applicants who were eligible and qualified for a mortgage after 3,700 applications were picked up in person by prospective buyers.

Now applicants with the highest lottery positions are beginning to select which unit they want, in the order their names were drawn.

The Howard Hughes Corp. expects it could take until Thursday for all of the applicants to select a unit — assuming the unit they are interested in is still available. It is estimated that 100 applicants will choose their units today.

There could be units left over after all 956 applicants have an opportunity to buy, given that many buyers might want the same units. Or the building could sell out before the list is exhausted.

Entrants or those who are curious to see which units get picked can visit kekilohana.com/residence-guide/#availability.

At the lottery Friday it took about three hours to draw slips of paper with each entrant’s name from a clear barrel in the lobby of the IBM Building in Kakaako, which serves as a sales office for Hughes Corp.

Todd Apo, vice president of community development for Hughes Corp., said about 75 applicants watched the drawing in person.

“Every once in a while you’d get a cheer from someone here with us who had their number pulled,” he said.

Ke Kilohana prices range from $323,475 to $442,246 for one-bedroom units, from $473,789 to $538,612 for two-bedroom units and from $521,774 to $560,774 for three-bedroom units.

Buyers may earn no more than 140 percent of Honolulu’s median income, an amount that equates to about $85,150 for a single person, $97,300 for a couple or $121,650 for a family of four.

The planned tower at 988 Halekauwila St. is being developed to satisfy an affordable-housing requirement in a Hughes Corp. master plan for up to 4,300 residences in 22 towers on 60 acres at what used to be Ward Centers.

The Hawaii Community Development Authority, a state agency that regulates development in Kakaako, requires 20 percent of all new high-rise homes in the area be affordable to a “gap group” of residents who often can’t afford market-priced homes but don’t qualify for other affordable-housing programs tailored to median- and low-income households.

Ke Kilohana has 424 units total, and 49 units will be priced at market rates without buyer restrictions and are expected to be sold later this year.

The restrictions on below-market units include the right for the HCDA to buy back units that initial buyers elect to sell within two to five years, and a requirement for initial buyers to pay the HCDA the difference between a unit’s original sale price and market price whenever the unit is first resold.