The nation's basic money supply grew by $3.8 billion for the latest statement week, the Federal Reserve Board reported yesterday in a development that seriously complicates the central bank's dilemma over how much further to raise interest rates.

The rise in the money supply - know as M-1, the sum of cash in circulation and checking account deposits - to a seasonally adjusted $364 billion for the week ended Oct. 11 means that the money base has grown at a 12 percent rate over the last month, at an 11 percent rate over the last two months and at a 9 percent rate over the last three months.

During this period the Fed has been actively raising short-term interest rates in an effort to control the money supply, but the growth rate has only been accelerating.

This latest jump puts the authorities into an increasingly embarrasing position," said Paine Webber economist Lawrence Kudlow, "because on the one hand the administration is trying to muster a credible anti-inflation policy, but one the other hand, the price of the dollar keeps falling, because an anti-inflation policy has no credibility as long as the monetary aggregated continue to rise at this rate."