How did the Government statistician get his figures in the smacking referendum petition?

There's been a bit of misinformation around the smacking petition. I've seen news reports, blogs and media releases that have both provided incorrect figures, while correctly stating that the petition has been deemed by the Government Statistician not to have a valid 10% of signatures. According to petitioners, they handed in 324,511 signatures on February 29,( not 324,316 as DPF noted). The sample was 1/11th - so 29,501 signatures were checked. That's a pretty high sample size meaning there is a higher margin of error. Of those signatures checked, 25,754 were valid, meaning 3,747 were not. Of those signatories not qualified 3,373 could not be found on the electoral roll, 214 were illegible, 158 were duplicated and 2 were triplicates. So 25,754 x 11 = 283,294. The number required is 285,027 so this indicates a shortfall of just 1,733 signatures, give or take errors. However the Government’s Statistician has said that his best estimate is just 266,903 or a shortfall of more than 18,000; nearly 17,300 greater than the 1/11th sample would indicate. The standard error is +/- 1600. The Government Statistician did a one sided hypothesis test at the 95% confidence level -and at the top confidence level (99%), that's 269,500. So why use the highest confidence level? How did he get his 266,903 number? He used the estimator of Goodman and Kiranandana. No idea what that is. Can anyone tell me?