fig1 shows a local clock 10 according to the present teachings . the local clock 10 includes a counter 12 that generates a time count 18 in response to an oscillator signal 16 from an oscillator 14 . the oscillator signal 16 causes the counter 12 to increment , e . g . on rising edges of the oscillator signal 16 . the local clock 10 includes a rate correction circuit 20 and an accumulator 22 that generate a local time 110 by accumulating a set of rate coefficients 100 in response to the time count 18 . the rate correction circuit 20 selects a sequence of rate coefficients 100 using a series of progressively longer replacement periods . the rate coefficients 100 may be referred to as a 0 , a 1 , . . . a m . the rate correction circuit 20 selects a coefficient 40 from among the rate coefficients a 0 , a 1 , . . . a m for accumulation by the accumulator 22 for each step in the time count 18 . table 1 shows the index i of the rate coefficient a i that is selected by the rate correction circuit 20 this embodiment in the time count 18 in one embodiment . in this embodiment , the rate coefficient a 1 replaces every 4th use of the rate coefficient a 0 . the rate coefficient a 2 replaces every 4th use of the rate coefficient a 1 , and so on . the allocation of the rate coefficients a 0 , a 1 , . . . a m to the steps in the count 18 provide a set of replacement periods . the replacement periods may be referred to as n 0 , n 1 . . . n m . the replacement periods n 0 , n 1 . . . n m in one embodiment are multiples of each other such that n j = k * n j + 1 , for all j where the multiplication factor k is a power of two . in the case of k = 4 , the local time 110 accumulates as a 0 , 2 * a 0 , 3 * a 0 , ( a 1 + 3 * a 0 ), ( a 1 + 4 * a 0 ), ( a 1 + 5 * a 0 ), ( a 1 + 6 * a 0 ) ( 2 * a 1 + 6 * a 0 ), . . . ( 3 * a 1 + 12 * a 0 ), ( a 2 + 3 * a 1 + 12 * a 0 ), ( a 2 + 3 * a 1 + 13 * a 0 ) and so on . each rate coefficient a 0 , a 1 , . . . a m has a range of zero to ( 2ˆk − 1 ). the rate coefficients a 0 , a 1 , . . . a m and the replacement periods n 0 , n 1 . . . n m yield an instantaneous quantization error in the local time 110 that does not exceed k / 2 times the rate coefficient lsb . each time the quantization error of the local time 110 approaches k / 2 times the rate coefficient lsb , another longer - period rate coefficient is invoked . in one embodiment , the counter 12 is a binary counter of length log 2 ( k * m ) bits . fig2 shows one embodiment of the rate correction circuit 20 . the rate correction circuit 20 includes a set of and gates 60 - 62 and a set of or gates 63 - 65 that implement a multiplexor and some enable logic 50 for the multiplexor . the enable logic 50 enables uses the and gates 60 - 62 to enable the rate coefficients a 0 , a 1 , . . . a m via a set of enable signals 70 - 72 ( enable 0 through enable m ). the enable logic 50 enables only one of the rate coefficients a 0 , a 1 , . . . a m at each step of the time count 18 . the or gates 63 - 65 provide the enabled rate coefficient 40 to the accumulator 22 . the enable signals 70 - 72 are determined by combining bits of the time count 18 . the enable signal 70 , enable 0 , for the 0th rate coefficient is ˜(˜ x 0 & amp ; ˜ x 1 & amp ; ˜ x 2 & amp ; . . . & amp ; ˜ x k − 2 & amp ; x k − 1 ). the enable signal enable i for the ith positive rate coefficient is (˜ x 0 & amp ; ˜ x 1 & amp ; ˜ x 2 & amp ; & amp ; ˜ x p − 2 & amp ; x p − 1 ) & amp ; ˜(˜ x p & amp ; ˜ x p + 1 & amp ; ˜ x p + 2 & amp ; . . . & amp ; ˜ x p + k − 2 & amp ; x p + k − 1 ), where p = i * k . in this equation , the x &# 39 ; s are the bit values of all of the stages of the counter 12 . in an embodiment in which k = 4 and m = 3 , the counter 12 is 12 - stage binary counter that derives the enable signals 70 - 72 for the four rate coefficients a 0 , a 1 , a 2 , and a 3 . the enable signals 70 - 72 for this embodiment are as follows . enable 0 =˜(˜ x 0 & amp ; ˜ x 1 & amp ; ˜ x 2 & amp ; x 3 ) enable 1 =(˜ x 0 & amp ; ˜ x 1 & amp ; ˜ x 2 & amp ; x 3 ) & amp ; ˜(˜ x 4 & amp ; ˜ x 5 & amp ; ˜ x 6 & amp ; x 7 ) enable 2 =(˜ x 0 & amp ; ˜ x 1 & amp ; ˜ x 2 & amp ; ˜ x 3 & amp ; ˜ x 4 & amp ; ˜ x 5 & amp ; ˜ x 6 & amp ; ˜ x 7 ) & amp ; ˜(˜ x 8 & amp ; ˜ x 9 & amp ; ˜ x 10 & amp ; x 11 ) enable 3 =(˜ x 0 & amp ; ˜ x 1 & amp ; ˜ x 2 & amp ; ˜ x 3 & amp ; ˜ x 4 & amp ; ˜ x 5 & amp ; ˜ x 6 & amp ; ˜ x 7 & amp ; ˜ x 8 & amp ; ˜ x 9 & amp ; ˜ x 10 & amp ; x 11 ) the rate correction circuit selects higher index rate coefficients with progressively less frequency . in the example embodiment set forth above , the a 0 rate coefficient is used 15 times for every 16 steps of the counter 12 . the a 1 rate coefficient is used 15 times for every 256 ( 16 * 16 ) steps of the counter 12 . the a 2 rate coefficient is used 15 times for every 4096 ( 16 * 16 * 16 ) steps of the counter 12 . the a 3 rate coefficient is used once every 4096 steps of the counter 12 . in an embodiment with an integer number of counter stages and k stages between each rate coefficient and a total of m + 1 rate coefficients , the number of times each rate coefficient is applied is n i =( k − 1 )* 2ˆ ( k * m )/ 2ˆ ( k *( i + 1 )) for i & lt ; m and n m = 1 . for the example above , the number of times each rate coefficient is selected is as follows . the local clock 10 improves quantization accuracy over the prior art technique of one correction per correction interval by a factor of k to the m power . the instantaneous accuracy of the local clock 10 is also high because the rate coefficients a 0 , a 1 , . . . a m are applied relatively frequently . additional rate coefficients may be used to decrease the value of k and therefore the maximum quantization error , but with an increase in hardware . if the replacement periods n 0 , n 1 . . . n m are not uniform multiples of each other , then the quantization error is corrected more frequently by some rate coefficients and less frequently by other rate coefficients . the rate coefficients a 0 , a 1 , . . . a m are selected to yield a final count f . the final count f may be derived from a time offset for correcting the local time 110 , e . g . during ieee 1588 time synchronization . the most frequently used rate coefficient is selected first and then the others are selected in sequence . the rate coefficients a 0 , a 1 , . . . a m are determined as follows . a 0 = floor ( f / n 0 ) a 1 = floor (( f − a 0 * n 0 )/ n 1 ) a 2 = floor (( f − a 0 * n 0 − a 1 * n 1 )/ n 2 ) a i = floor (( f − a 0 * n 1 . . . − a i − 1 * n i − 1 )/ n i ) for the example above , with a final count f equal to 16 , 793 , then the rate coefficients a 0 , a 1 , . . . a m are as follows . alternative counting schemes may be used in the local clock 10 , but at the expense of more complicated rate coefficient selection logic . counting schemes in which the frequency of rate coefficient use does not decrease geometrically with rate coefficient number will make suboptimal use of the rate coefficients by allowing more error . the foregoing detailed description of the present invention is provided for the purposes of illustration and is not intended to be exhaustive or to limit the invention to the accurate embodiment disclosed . accordingly , the scope of the present invention is defined by the appended claims .