Difference families of (q, 7,1)

This page provides some difference families of type (q,7,1) with q prime. Difference families in P_7 are as follows. Let c be a primitive cube root of unity in GF(q) and B = {0, 1, c, c^2, x, xc, xc^2}. Then the difference family is sB for s in S, S a system of representatives for the coset of H^7/H^{(q-1)/6}. In the following table we list q, x and c.

  1. 15000 <= q <= 500000
  2. 500000 <= q <= 5000000
  3. 5000000 <= q <= 6000000
  4. 6000000 <= q <= 7500000
  5. 7500000 <= q <= 8700000
  6. 8700000 <= q <= 10800000
  7. 10800000 <= q <= 13000000
  8. 13000000 <= q <= 34467049
The difference families not in P_7 are as follows. Let B = {0,1,b_1,b_2,b_3,b_4,b_5} or B={0,1,x,x^2,x^3,x^4,x^5}. Then the sB for s in S is the difference family. We list q and b_1,b_2,b_3,b_4,b_5 or x in the following tables
  1. 50000 <= q <= 2000000
  2. 2000000 <= q <= 7000000
  3. 7000000 <= q <= 12000000
  4. 12000000 <= q <= 16000000
  5. 16000000 <= q <= 21000000
  6. 21000000 <= q <= 25000000
  7. 25000000 <= q <= 30000000
  8. 30000000 <= q <= 35000000
  9. 34103935 <= q <= 76438657
  10. 76440883 <= q <= 126839749
  11. 126841303 <= q <= 177236011
  12. 177241261 <= q <= 227639539
  13. 227640631 <= q <= 261239791
For the details of the construction see here.

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