Sydney - Ricky Ponting, Australia's greatest run-scorer, hailed Steve Smith as "a genius" on Friday after his Ashes double hundred - an exploit his country's media said was "Donald Bradman-like".

Smith has taken his game to a new level since returning from a 12-month ball-tampering ban this year, with his 211 in the fourth Test at Old Trafford giving him an incredible batting average during the series of 147.25.

"You hear all sorts of words, 'genius' is one that comes to mind," Ponting told cricket.com.au when asked to sum up Smith's knock, which put Australia in a dominant position after two days.

"A remarkable innings again. It's his application to what he does. He just doesn't make any mistakes. His concentration levels are obviously unbelievably good."

Even Ponting, one of cricket's sharpest minds, struggled to think of how to get him out. But he did have some advice.

"He's only been out nine times lbw in his last 99 innings, so you know if you're bowling straight you're not going to get him out," he said.

"The one thing you have to do is try and challenge the outside of his bat. He doesn't miss it on the inside."

Smith, who last week regained first place in the ICC Test batting rankings ahead of India's Virat Kohli, is increasingly being compared to legendary countryman Bradman, widely considered Test cricket's best ever.

Ponting pointed out that only Bradman had scored more centuries and double centuries against England, and only Bradman had a higher batting average (99.94) than Smith's current 64.64.

"Even what Smithy is doing now is remarkable, to think how good Bradman must have been to be a third again better than what Steve Smith's doing at the moment is ridiculous," he said.

Australia's media said the gap between the two men was constantly narrowing.

"We're at the point where Smith and Bradman can not only be used in the same sentence but transposed," said The Australian's senior cricket writer, Gideon Haigh.

The Sydney Daily Telegraph was equally effusive in its praise of Smith's batting, which has seen three centuries in four innings this series following scores of 144 and 142. His worst knock was 92.

"Double ton confirms Smith's greatness," the tabloid said in its headline.

"His score of 211 was an innings beyond significance for the match alone, it was one which took the batting genius beyond comparisons with anyone other than Sir Donald Bradman," it said.