Short table of parameters for generalised Marsaglia's Xorshift RNG. For terminology, see the comments in xorgens200.c. More extensive tables are available from the author. For wordlengths w = 32 and 64 we give solutions for n = w*r of the form n = 2^k (k le 12) and the other known solutions for n gt 2^12. The solutions (r, s, a, b, c, d) satisfy the following constraints: a + b le w, c + d le w, (a, b, c, d) all distinct, GCD(a,b) = GCD(c,d) = GCD(r,s) = 1, a gt b, c lt d. Minimal polynomial primitive of degree n, so the period is 2^n - 1. Let delta = min (a, b, c, d) and Wt = number of nonzero terms in the minimal polynomial. The solutions given are "best" in the sense of having maximal delta subject to the above constraints. In the case of ties we also maximise Wt. NB: The programs in xorgens200.c assume that n is a power of two. Some small modifications need to be made for n = 4224 or 4480. w = 32: n 64 w 32 r 2 s 1 a 17 b 14 c 12 d 19 Wt 31 delta 12 n 128 w 32 r 4 s 3 a 15 b 14 c 12 d 17 Wt 55 delta 12 n 256 w 32 r 8 s 3 a 18 b 13 c 14 d 15 Wt 109 delta 13 n 512 w 32 r 16 s 1 a 17 b 15 c 13 d 14 Wt 185 delta 13 n 1024 w 32 r 32 s 15 a 19 b 11 c 13 d 16 Wt 225 delta 11 n 2048 w 32 r 64 s 59 a 19 b 12 c 14 d 15 Wt 213 delta 12 n 4096 w 32 r 128 s 95 a 17 b 12 c 13 d 15 Wt 251 delta 12 n 4224 w 32 r 132 s 67 a 15 b 14 c 13 d 18 Wt 243 delta 13 n 4480 w 32 r 140 s 19 a 17 b 13 c 15 d 16 Wt 251 delta 13 w = 64: n 128 w 64 r 2 s 1 a 33 b 31 c 28 d 29 Wt 65 delta 28 n 256 w 64 r 4 s 3 a 37 b 27 c 29 d 33 Wt 127 delta 27 n 512 w 64 r 8 s 1 a 37 b 26 c 29 d 34 Wt 231 delta 26 n 1024 w 64 r 16 s 7 a 34 b 29 c 25 d 31 Wt 439 delta 25 n 2048 w 64 r 32 s 1 a 35 b 27 c 26 d 37 Wt 745 delta 26 n 4096 w 64 r 64 s 53 a 33 b 26 c 27 d 29 Wt 961 delta 26 n 4224 w 64 r 66 s 41 a 33 b 31 c 27 d 29 Wt 987 delta 27 n 4480 w 64 r 70 s 61 a 34 b 29 c 30 d 31 Wt 951 delta 29 R. P. Brent, 20040812