Ballots should be considered for allocating places at the country's top state schools to give disadvantaged pupils more equal access, according to a new report.

The study, published by the Sutton Trust, found the top performing 70 state schools in Scotland take half as many disadvantaged pupils as the national average and the school system is "highly socially segregated".

These top schools have an average of 8.2% of pupils who are registered for free school meals (FSM), about half of the average rate for all schools nationally (16.3%), the report found.

Revealed: Top state schools in Scotland

The report, by researchers at the National Foundation for Educational Research (NFER), found high-performing Scottish schools are quite reflective of their local area, with around four out of five top performing schools ranked in the 40% most affluent areas of the country.

While 57% of top performing schools take slightly fewer disadvantaged pupils than their catchment area, 39% take slightly more.

The Sutton Trust is now calling for changes to the admissions process that include considering the level of socioeconomic diversity when drawing up catchment areas.

In the longer term, the report recommends the Scottish Government, local councils and schools consider a system with fewer incentives for middle class parents to buy homes in the catchment areas of top schools.

Allocating a proportion of places randomly, such as half through a ballot system, could form a central part of this approach.

Read more: Scratch beneath surface to find real top schools

Sir Peter Lampl, founder and chairman of the Sutton Trust, said: "Getting a place at a good school is key to getting on in life.

"Yet the bottom line is that in Scotland your chances of doing that depends on your parents' income and whether they can afford to live in an affluent area.

"This is why we want to see more use of ballots - where a proportion of places is allocated randomly - as well as a focus on improving the quality of teaching in all schools, particularly those in the most disadvantaged areas."

The 70 top performing state schools in Scotland were calculated based on the proportion of pupils achieving at least 4 A to C grades in their SCQF level 5 qualifications.

The report also recommended deprived families should receive greater support in terms of transport to enable children to attend a school outwith their immediate area, and there should be a focus on improving standards at schools in deprived areas.

Deputy First Minister John Swinney said: "This report highlights that the poverty-related attainment gap is faced across the UK.

"We want to see excellence for every pupil, in every school, and are investing £750 million in the Scottish Attainment Challenge to narrow the gap between pupils from the most and least deprived communities.

Latest data shows improvements with the gap closing among pupils at Higher level and among young people going on to study, train or work.

Read more: Schools in deprived areas real winners in league tables

"Schools should serve everyone in their community and a ballot process would completely undermine that link."

Scottish Labour education spokesman Iain Gray MSP said: "Scottish Labour strongly supports local schools serving their local communities and does not support changing that.

"But this report does provide more evidence of what Labour has been saying for some time - that there is a shocking attainment gap between the richest and poorest children in our communities.

"Another generation are being left behind despite the promises from SNP politicians."